| Title: | Advanced L-Moment Fitting of Distributions |
|---|---|
| Description: | A complete framework for frequency analysis is provided by 'LMoFit'. It has functions related to the determination of sample L-moments as in Hosking, J.R.M. (1990) <doi:10.1111/j.2517-6161.1990.tb01775.x>, the fitting of various distributions as in Zaghloul et al. (2020) <doi:10.1016/j.advwatres.2020.103720> and Hosking, J.R.M. (2019) <https://CRAN.R-project.org/package=lmom>, besides plotting and manipulating L-space diagrams as in Papalexiou, S.M. & Koutsoyiannis, D. (2016) <doi:10.1016/j.advwatres.2016.05.005> for two-shape parametric distributions on the L-moment ratio diagram. Additionally, the quantile, probability density, and cumulative probability functions of various distributions are provided in a user-friendly manner. |
| Authors: | Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths] |
| Maintainer: | Mohanad Zaghloul <[email protected]> |
| License: | GPL-3 |
| Version: | 0.1.7 |
| Built: | 2025-03-10 02:33:28 UTC |
| Source: | https://github.com/cran/LMoFit |
Comparing sample L-moment ratios with L-spaces of various distributions on the L-moments ratio diagram
com_sam_lspace(sample, type = "m", Dist = "BrIII", color = "red", shape = 8)com_sam_lspace(sample, type = "m", Dist = "BrIII", color = "red", shape = 8)
sample |
for a single site, sample is a vector of observations, e.x. FLOW_AMAX. For multiple sites, sample is a dataframe consisting of multiple columns where each column has the data observed at one site; this dataframe should have column names as station names, e.x. FLOW_AMAX_MULT. |
type |
the type of the sample. It can be "s" for single site, the default, or "m" for multiple sites. |
Dist |
select the distribution to plot its L-space in the background. This can be "BrIII" for Burr Typr-III distribution, "BrXII" for Burr Typr-XII distribution, or "GG" for Generalized Gamma distribution. The default Dist is "BrIII". |
color |
color of the L-point/s, default is "red". |
shape |
shape of the L-point/s, default is 8. |
ggplot plot comparing sample/s L-point/s with L-space of a distribution on the L-moment ratio diagram
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
com_plot_BrIII <- com_sam_lspace(LMoFit::FLOW_AMAX, type = "s", Dist = "BrIII") com_plot_BrXII <- com_sam_lspace(LMoFit::FLOW_AMAX, type = "s", Dist = "BrXII") com_plot_GG <- com_sam_lspace(LMoFit::FLOW_AMAX, type = "s", Dist = "GG") com_plot_BrIII <- com_sam_lspace(LMoFit::FLOW_AMAX_MULT, type = "m", Dist = "BrIII") com_plot_BrXII <- com_sam_lspace(LMoFit::FLOW_AMAX_MULT, type = "m", Dist = "BrXII") com_plot_GG <- com_sam_lspace(LMoFit::FLOW_AMAX_MULT, type = "m", Dist = "GG")com_plot_BrIII <- com_sam_lspace(LMoFit::FLOW_AMAX, type = "s", Dist = "BrIII") com_plot_BrXII <- com_sam_lspace(LMoFit::FLOW_AMAX, type = "s", Dist = "BrXII") com_plot_GG <- com_sam_lspace(LMoFit::FLOW_AMAX, type = "s", Dist = "GG") com_plot_BrIII <- com_sam_lspace(LMoFit::FLOW_AMAX_MULT, type = "m", Dist = "BrIII") com_plot_BrXII <- com_sam_lspace(LMoFit::FLOW_AMAX_MULT, type = "m", Dist = "BrXII") com_plot_GG <- com_sam_lspace(LMoFit::FLOW_AMAX_MULT, type = "m", Dist = "GG")
Condition of sample lpoints, as inside/outside of specific L-spaces on the L-moments ratio diagram, using sample.
con_sam_lspace(sample, type = "s", Dist = "BrIII")con_sam_lspace(sample, type = "s", Dist = "BrIII")
sample |
for a single site, sample is a vector of observations, e.x. FLOW_AMAX. For multiple sites, sample is a dataframe consisting of multiple columns where each column has the data observed at one site; this dataframe should have column names as station names, e.x. FLOW_AMAX_MULT. |
type |
the type of the sample. It can be "s" for single site, the default, or "m" for multiple sites. |
Dist |
select the distribution to plot its L-space in the background. This can be "BrIII" for Burr Typr-III distribution, "BrXII" for Burr Typr-XII distribution, or "GG" for Generalized Gamma distribution. The default Dist is "BrIII". |
The condition of the L-points in regards to the selected L-space as inside or outside.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
con_sam_lspace(LMoFit::FLOW_AMAX, type = "s", Dist = "BrIII") con_sam_lspace(LMoFit::FLOW_AMAX, type = "s", Dist = "BrXII") con_sam_lspace(LMoFit::FLOW_AMAX, type = "s", Dist = "GG") con_sam_lspace(LMoFit::FLOW_AMAX_MULT, type = "m", Dist = "BrIII") con_sam_lspace(LMoFit::FLOW_AMAX_MULT, type = "m", Dist = "BrXII") con_sam_lspace(LMoFit::FLOW_AMAX_MULT, type = "m", Dist = "GG")con_sam_lspace(LMoFit::FLOW_AMAX, type = "s", Dist = "BrIII") con_sam_lspace(LMoFit::FLOW_AMAX, type = "s", Dist = "BrXII") con_sam_lspace(LMoFit::FLOW_AMAX, type = "s", Dist = "GG") con_sam_lspace(LMoFit::FLOW_AMAX_MULT, type = "m", Dist = "BrIII") con_sam_lspace(LMoFit::FLOW_AMAX_MULT, type = "m", Dist = "BrXII") con_sam_lspace(LMoFit::FLOW_AMAX_MULT, type = "m", Dist = "GG")
Condition of sample lpoints, as inside/outside of specific L-spaces on the L-moments ratio diagram, using sample lmoments.
con_samlmom_lspace(samplelmom, Dist = "BrIII")con_samlmom_lspace(samplelmom, Dist = "BrIII")
samplelmom |
L-moments as c(l1, l2, l3, l4, t2, t3, t4). Use get_sample_lmom() to obtain these lmoments. |
Dist |
select the distribution to plot its L-space in the background. This can be "BrIII" for Burr Typr-III distribution, "BrXII" for Burr Typr-XII distribution, or "GG" for Generalized Gamma distribution. The default Dist is "BrIII". The default is set to BrIII. |
The condition of the L-points in regards to the selected L-space as inside or outside.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
sample <- LMoFit::FLOW_AMAX samplelmom <- get_sample_lmom(x = sample) con_samlmom_lspace(samplelmom, Dist = "BrIII") con_samlmom_lspace(samplelmom, Dist = "BrXII") con_samlmom_lspace(samplelmom, Dist = "GG")sample <- LMoFit::FLOW_AMAX samplelmom <- get_sample_lmom(x = sample) con_samlmom_lspace(samplelmom, Dist = "BrIII") con_samlmom_lspace(samplelmom, Dist = "BrXII") con_samlmom_lspace(samplelmom, Dist = "GG")
Probability density function of BrIII distribution
dBrIII(x, para = c(1, 2, 0.5))dBrIII(x, para = c(1, 2, 0.5))
x |
quantile/s |
para |
parameters as c(scale, shape1, shape2) |
Probability density function
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
d <- dBrIII(x = 108.4992, para = c(10, 0.25, 0.5))d <- dBrIII(x = 108.4992, para = c(10, 0.25, 0.5))
Probability density function of BrXII distribution
dBrXII(x, para = c(1, 2, 0.5))dBrXII(x, para = c(1, 2, 0.5))
x |
quantile/s |
para |
parameters as c(scale, shape1, shape2) |
Probability density function
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
d <- dBrXII(x = 108.4992, para = c(10, 0.25, 0.5))d <- dBrXII(x = 108.4992, para = c(10, 0.25, 0.5))
Probability density function of Gamma distribution
dgam(x, para = c(1, 2, 0.5))dgam(x, para = c(1, 2, 0.5))
x |
quantile/s |
para |
parameters as c(shape, scale) |
Probability density function
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
d <- dgam(x = 0.1, para = c(0.1, 0.2))d <- dgam(x = 0.1, para = c(0.1, 0.2))
Probability density function of GEV distribution
dgev(x, para)dgev(x, para)
x |
quantile/s |
para |
parameters as c(location, scale, shape) |
Probability density function
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
d <- dgev(x = 108.4992, para = c(10, 1, 1))d <- dgev(x = 108.4992, para = c(10, 1, 1))
Probability density function of Generalized Gamma (GG) distribution
dGG(x, para = c(10, 0.25, 0.5))dGG(x, para = c(10, 0.25, 0.5))
x |
quantile/s |
para |
parameters as c(scale, shape1, shape2) |
Probability density function
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
d <- dGG(x = 108.4992, para = c(10, 0.25, 0.5))d <- dGG(x = 108.4992, para = c(10, 0.25, 0.5))
Probability density function of Generalized Logestic Distribution
dglo(x, para = c(1, 2, 0.5))dglo(x, para = c(1, 2, 0.5))
x |
quantile/s |
para |
parameters as c(location, scale, shape) |
Probability density function
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
d <- dglo(x = 0.1, para = c(1, 2, 0.5))d <- dglo(x = 0.1, para = c(1, 2, 0.5))
Probability density function of Generalized normal Distribution
dgno(x, para = c(1, 2, 0.5))dgno(x, para = c(1, 2, 0.5))
x |
quantile/s |
para |
parameters as c(location, scale, shape) |
Probability density function
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
d <- dgno(x = 0.1, para = c(1, 2, 0.5))d <- dgno(x = 0.1, para = c(1, 2, 0.5))
Probability density function of Generalized Pareto Distribution
dgpa(x, para)dgpa(x, para)
x |
quantile/s |
para |
parameters as c(location, scale, shape) |
Probability density function
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
d <- dgpa(x = 0.1, para = c(1, 2, 0.5))d <- dgpa(x = 0.1, para = c(1, 2, 0.5))
Probability density function of Lognormal-3 Distribution
dln3(x, para = c(0, 0, 1))dln3(x, para = c(0, 0, 1))
x |
quantile/s |
para |
parameters as c(zeta, mu, sigma) that is c(lower bound, mean on log scale, standard deviation on log scale). |
Probability density function
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
d <- dln3(x = 12, para = c(0, 0, 1))d <- dln3(x = 12, para = c(0, 0, 1))
Probability density function of Normal Distribution
dnor(x, para = c(1, 2))dnor(x, para = c(1, 2))
x |
quantile/s |
para |
parameters as c(location, scale) |
Probability density function
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
d <- dnor(x = 1.5, para = c(1, 2))d <- dnor(x = 1.5, para = c(1, 2))
Probability density function of Pearson type-3 Distribution
dpe3(x, para = c(10, 1, 1.5))dpe3(x, para = c(10, 1, 1.5))
x |
quantile/s |
para |
parameters as c(mu, sigma, gamma) that is c(location, scale, shape). |
Probability density function
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
d <- dpe3(x = 12, para = c(10, 1, 1.5))d <- dpe3(x = 12, para = c(10, 1, 1.5))
Fit Burr Type-III (BrIII) Distribution
fit_BrIII(sl1, st2, st3)fit_BrIII(sl1, st2, st3)
sl1 |
1st l-moments |
st2 |
2nd l-moment ratio |
st3 |
3rd l-moment ratio |
A dataframe containing the scale parameter, the shape1 parameter, the shape2 parameter, the squared error of scale parameter, and the squared error of shape parameter
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
BrIII_par_valid <- fit_BrIII(sl1 = 10, st2 = 0.25, st3 = 0.1) BrIII_par_invalid <- fit_BrIII(sl1 = 10, st2 = 0.5, st3 = 0.8)BrIII_par_valid <- fit_BrIII(sl1 = 10, st2 = 0.25, st3 = 0.1) BrIII_par_invalid <- fit_BrIII(sl1 = 10, st2 = 0.5, st3 = 0.8)
Fit Burr Type-XII (BrXII) Distribution
fit_BrXII(sl1, st2, st3)fit_BrXII(sl1, st2, st3)
sl1 |
1st l-moments |
st2 |
2nd l-moment ratio |
st3 |
3rd l-moment ratio |
A dataframe containing the scale parameter, the shape1 parameter, the shape2 parameter, the squared error of the scale parameter, and the squared error of the shape parameters.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
BrXII_par_valid <- fit_BrXII(sl1 = 10, st2 = 0.25, st3 = 0.25) BrXII_par_invalid <- fit_BrXII(sl1 = 10, st2 = 0.5, st3 = 0.8)BrXII_par_valid <- fit_BrXII(sl1 = 10, st2 = 0.25, st3 = 0.25) BrXII_par_invalid <- fit_BrXII(sl1 = 10, st2 = 0.5, st3 = 0.8)
Fit Gamma distribution using the 'lmom' package
fit_gam(sl1, sl2, st3, st4)fit_gam(sl1, sl2, st3, st4)
sl1 |
sample 1st l-moment |
sl2 |
sample 2nd l-moment |
st3 |
sample 3rd l-moment ratio |
st4 |
sample 4th l-moment ratio |
A vector of parameters as alpha (shape) and beta (scale).
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
gam_par <- fit_gam(15, 1.7, 0.04, -0.02)gam_par <- fit_gam(15, 1.7, 0.04, -0.02)
Fit GEV distribution
fit_gev(sl1, sl2, st3)fit_gev(sl1, sl2, st3)
sl1 |
sample 1st l-moment |
sl2 |
sample 2nd l-moment |
st3 |
sample 3rd l-moment ratio |
A dataframe containing the location parameter, the scale parameter, the shape parameter, and the squared error of shape parameters.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
GEV_par <- fit_gev(sl1 = 10, sl2 = 0.5, st3 = 0.8)GEV_par <- fit_gev(sl1 = 10, sl2 = 0.5, st3 = 0.8)
Fit Generalized Gamma (GG) Distribution
fit_GG(sl1, st2, st3)fit_GG(sl1, st2, st3)
sl1 |
1st l-moments |
st2 |
2nd l-moment ratio |
st3 |
3rd l-moment ratio |
A dataframe containing the scale parameter, the shape1 parameter, the shape2 parameter, the squared error of scale parameter, and the squared error of shape parameters.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
GG_par_valid <- fit_GG(sl1 = 10, st2 = 0.4, st3 = 0.2) GG_par_invalid <- fit_GG(sl1 = 1, st2 = 0.25, st3 = 0.25)GG_par_valid <- fit_GG(sl1 = 10, st2 = 0.4, st3 = 0.2) GG_par_invalid <- fit_GG(sl1 = 1, st2 = 0.25, st3 = 0.25)
Fit Generalized Logistic distribution using the 'lmom' package
fit_glo(sl1, sl2, st3, st4)fit_glo(sl1, sl2, st3, st4)
sl1 |
sample 1st l-moment |
sl2 |
sample 2nd l-moment |
st3 |
sample 3rd l-moment ratio |
st4 |
sample 4th l-moment ratio |
A vector of parameters as xi (location), alpha (scale), and k (shape).
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
glo_par <- fit_glo(15, 1.7, 0.04, -0.02)glo_par <- fit_glo(15, 1.7, 0.04, -0.02)
Fit Generalized Normal distribution using the 'lmom' package
fit_gno(sl1, sl2, st3, st4)fit_gno(sl1, sl2, st3, st4)
sl1 |
sample 1st l-moment |
sl2 |
sample 2nd l-moment |
st3 |
sample 3rd l-moment ratio |
st4 |
sample 4th l-moment ratio |
A vector of parameters as xi (location), alpha (scale), and k (shape).
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
gno_par <- fit_gno(15, 1.7, 0.04, -0.02)gno_par <- fit_gno(15, 1.7, 0.04, -0.02)
Fit Generalized Pareto distribution using the 'lmom' package
fit_gpa(sl1, sl2, st3, st4)fit_gpa(sl1, sl2, st3, st4)
sl1 |
sample 1st l-moment |
sl2 |
sample 2nd l-moment |
st3 |
sample 3rd l-moment ratio |
st4 |
sample 4th l-moment ratio |
A vector of parameters as xi (location), alpha (scale), and k (shape).
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
gpa_par <- fit_gpa(15, 1.7, 0.04, -0.02)gpa_par <- fit_gpa(15, 1.7, 0.04, -0.02)
Fit LogNormal-3 distribution using the 'lmom' package
fit_ln3(sl1, sl2, st3, st4)fit_ln3(sl1, sl2, st3, st4)
sl1 |
sample 1st l-moment |
sl2 |
sample 2nd l-moment |
st3 |
sample 3rd l-moment ratio |
st4 |
sample 4th l-moment ratio |
A vector of parameters as zeta (lower bound), mu (mean on log-scale), and sigma (st.dev. on log-scale)
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
ln3_par <- fit_ln3(15, 1.7, 0.04, -0.02)ln3_par <- fit_ln3(15, 1.7, 0.04, -0.02)
Fit Normal distribution using the 'lmom' package
fit_nor(sl1, sl2, st3, st4)fit_nor(sl1, sl2, st3, st4)
sl1 |
sample 1st l-moment |
sl2 |
sample 2nd l-moment |
st3 |
sample 3rd l-moment ratio |
st4 |
sample 4th l-moment ratio |
A vector of parameters as mu (location) and sigma (scale).
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
nor_par <- fit_nor(15, 1.7, 0.04, -0.02)nor_par <- fit_nor(15, 1.7, 0.04, -0.02)
Fit Pearson Type-3 distribution using the 'lmom' package
fit_pe3(sl1, sl2, st3, st4)fit_pe3(sl1, sl2, st3, st4)
sl1 |
sample 1st l-moment |
sl2 |
sample 2nd l-moment |
st3 |
sample 3rd l-moment ratio |
st4 |
sample 4th l-moment ratio |
A vector of parameters as mu (location), sigma (scale), and gamma (shape).
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
pe3_par <- fit_pe3(15, 1.7, 0.04, -0.02)pe3_par <- fit_pe3(15, 1.7, 0.04, -0.02)
Annual maximum flow data at Water Survey of Canada WSC flow gauge number 08NA002 in BC, Vancouver, Canada. Lat: 51°14'36.8¨ N, Long: 116°54'46.6¨ W.
FLOW_AMAXFLOW_AMAX
A vector of observations of length equal to 112
annual maximum flow observed per each year at one site
coded in data-raw
Annual maximum flow data at 10 hypothetical flow gauge.
FLOW_AMAX_MULTFLOW_AMAX_MULT
A data frame with 112 rows and 10 variables:
annual maximum flow observed per each year at site 1
annual maximum flow observed per each year at site 2
annual maximum flow observed per each year at site 3
annual maximum flow observed per each year at site 4
annual maximum flow observed per each year at site 5
annual maximum flow observed per each year at site 6
annual maximum flow observed per each year at site 7
annual maximum flow observed per each year at site 8
annual maximum flow observed per each year at site 9
annual maximum flow observed per each year at site 10
coded in data-raw
Get julian date from the begining of the year
get_julian(x)get_julian(x)
x |
date or a series of dates such as, as.Date("yyyy-mm-dd") |
A julian date between 1 and 365, note that in leap years the day 366 is considered as 365
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
get_julian(x = as.Date("1979-01-15"))get_julian(x = as.Date("1979-01-15"))
Estimate sample L-moments and L-moment ratios
get_sample_lmom(x)get_sample_lmom(x)
x |
a series of quantiles |
A dataframe containing the 1st l-moment, the 2nd l-moment, the 3rd l-moment, the 4th l-moment, the 2nd l-moment ratio "L-variation", the 3rd l-moment ratio "L-skewness", and the 4th l-moment ratio "L-kurtosis"
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
sample_lmom <- get_sample_lmom((rnorm(n = 500, mean = 10, sd = 0.5)))sample_lmom <- get_sample_lmom((rnorm(n = 500, mean = 10, sd = 0.5)))
This is a plot of the L-space of BrIII Distribution with L-variation on x-axis and L-skewness on y-axis. The L-space is bounded by shape1 in the range of 0.01 to 150.01, and by shape2 in the range of 0.005 to 0.999.
lspace_BrIIIlspace_BrIII
A ggplot
coded in data-raw
This is a plot of the L-space of BrIII Distribution with L-variation on x-axis and L-skewness on y-axis. The L-space is bounded by shape1 in the range of 0.01 to 150.01, and by shape2 in the range of 0.005 to 0.999.
lspace_BrIII.xylspace_BrIII.xy
A ggplot
l-variatoin "t2"
l-skewness "t3"
coded in data-raw
This is a plot of the L-space of BrXII Distribution with L-variation on x-axis and L-skewness on y-axis. The L-space is bounded by shape1 in the range of 0.1 to 150, and by shape2 in the range of 0.001 to 1.
lspace_BrXIIlspace_BrXII
A ggplot
coded in data-raw
This is a plot of the L-space of BrXII Distribution with L-variation on x-axis and L-skewness on y-axis. The L-space is bounded by shape1 in the range of 0.1 to 150, and by shape2 in the range of 0.001 to 1.
lspace_BrXII.xylspace_BrXII.xy
A ggplot
l-variatoin "t2"
l-skewness "t3"
coded in data-raw
This is a plot of the L-space of GG Distribution with L-variation on x-axis and L-skewness on y-axis. The L-space is bounded by shape1 in the range of 0.1 to 5.9, and by shape2 in the range of 0.19 to 38.
lspace_GGlspace_GG
A ggplot
coded in data-raw
This is a plot of the L-space of GG Distribution with L-variation on x-axis and L-skewness on y-axis. The L-space is bounded by shape1 in the range of 0.1 to 5.9, and by shape2 in the range of 0.19 to 38.
lspace_GG.xylspace_GG.xy
A ggplot
l-variatoin "t2"
l-skewness "t3"
coded in data-raw
Cumulative distribution function of BrIII distribution
pBrIII(x, para = c(1, 2, 0.5))pBrIII(x, para = c(1, 2, 0.5))
x |
quantile/s |
para |
parameters as c(scale, shape1, shape2) |
Non-exceedance probability from the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
u <- pBrIII(x = 108.4992, para = c(10, 0.25, 0.5))u <- pBrIII(x = 108.4992, para = c(10, 0.25, 0.5))
Cumulative distribution function of BrXII distribution
pBrXII(x, para = c(1, 2, 0.5))pBrXII(x, para = c(1, 2, 0.5))
x |
quantile/s |
para |
parameters as c(scale, shape1, shape2) |
Non-exceedance probability from the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
u <- pBrXII(x = 108.4992, para = c(10, 0.25, 0.5))u <- pBrXII(x = 108.4992, para = c(10, 0.25, 0.5))
Emperical cumulative distribution function
pemp(data)pemp(data)
data |
quantile/s |
A dataframe containing two columns as the sorted observations and the corresponding empirical probability of non-exceedance
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
output <- pemp(data = runif(n = 50, min = 10, max = 100))output <- pemp(data = runif(n = 50, min = 10, max = 100))
Cumulative distribution function of Gamma distribution
pgam(x, para = c(1.5, 1))pgam(x, para = c(1.5, 1))
x |
quantile/s |
para |
parameters as c(shape, scale) |
Non-exceedance probability from the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
u <- pgam(x = 0.1, para = c(0.1, 0.2))u <- pgam(x = 0.1, para = c(0.1, 0.2))
Cumulative distribution function of GEV distribution
pgev(x, para)pgev(x, para)
x |
quantile/s |
para |
parameters as c(location, scale, shape) |
Non-exceedance probability from the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
u <- pgev(x = 108.4992, para = c(10, 1, 1))u <- pgev(x = 108.4992, para = c(10, 1, 1))
Cumulative distribution function of Generalized Gamma (GG) distribution
pGG(x, para = c(10, 0.25, 0.5))pGG(x, para = c(10, 0.25, 0.5))
x |
quantile/s |
para |
parameters as c(scale, shape1, shape2) |
Non-exceedance probability from the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
u <- pGG(x = 108.4992, para = c(10, 0.25, 0.5))u <- pGG(x = 108.4992, para = c(10, 0.25, 0.5))
Cumulative distribution function of Generalized Logistic Distribution
pglo(x, para = c(10, 1.5, 1))pglo(x, para = c(10, 1.5, 1))
x |
quantile/s |
para |
parameters as c(location, scale, shape) |
Non-exceedance probability from the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
u <- pglo(x = 0.1, para = c(10, 0.1, 0.2))u <- pglo(x = 0.1, para = c(10, 0.1, 0.2))
Cumulative distribution function of Generalized Normal Distribution
pgno(x, para = c(10, 1.5, 1))pgno(x, para = c(10, 1.5, 1))
x |
quantile/s |
para |
parameters as c(location, scale, shape) |
Non-exceedance probability from the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
u <- pgno(x = 10.1, para = c(10, 0.1, 0.2))u <- pgno(x = 10.1, para = c(10, 0.1, 0.2))
Cumulative distribution function of Generalized Pareto Distribution
pgpa(x, para = c(1, 1, 1))pgpa(x, para = c(1, 1, 1))
x |
quantile/s |
para |
parameters as c(location, scale, shape) |
Non-exceedance probability from the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
u <- pgpa(x = 1.2, para = c(1, 2, 0.5))u <- pgpa(x = 1.2, para = c(1, 2, 0.5))
Cumulative distribution function of Lognormal-3 Distribution
pln3(x, para = c(0, 0, 1))pln3(x, para = c(0, 0, 1))
x |
quantile/s |
para |
parameters as c(zeta, mu, sigma) that is c(lower bound, mean on log scale, standard deviation on log scale). |
Non-exceedance probability from the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
u <- pln3(x = 12, para = c(0, 0, 1))u <- pln3(x = 12, para = c(0, 0, 1))
Cumulative distribution function of Noramal Distribution
pnor(x, para = c(10, 1.5))pnor(x, para = c(10, 1.5))
x |
quantile/s |
para |
parameters as c(location, scale) |
Non-exceedance probability from the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
u <- pnor(x = 11, para = c(10, 1.5))u <- pnor(x = 11, para = c(10, 1.5))
Cumulative distribution function of Pearson type-3 Distribution
ppe3(x, para = c(10, 1, 1.5))ppe3(x, para = c(10, 1, 1.5))
x |
quantile/s |
para |
parameters as c(mu, sigma, gamma) that are c(location, scale, shape). |
Non-exceedance probability from the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
u <- ppe3(x = 12, para = c(10, 1, 1.5))u <- ppe3(x = 12, para = c(10, 1, 1.5))
Quantile distribution function of BrIII distribution
qBrIII(u = NULL, RP = 1/(1 - u), para)qBrIII(u = NULL, RP = 1/(1 - u), para)
u |
non-exceedance probability |
RP |
Return Period "don't use in case u is used" |
para |
parameters as c(scale, shape1, shape2) |
Quantile value/s using the inverse of the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
x <- qBrIII(u = 0.99, para = c(1, 10, 0.8)) x <- qBrIII(RP = 100, para = c(1, 10, 0.8))x <- qBrIII(u = 0.99, para = c(1, 10, 0.8)) x <- qBrIII(RP = 100, para = c(1, 10, 0.8))
Quantile distribution function of BrXII distribution
qBrXII(u = NULL, RP = 1/(1 - u), para)qBrXII(u = NULL, RP = 1/(1 - u), para)
u |
non-exceedance probability |
RP |
Return Period "don't use in case u is used" |
para |
parameters as c(scale, shape1, shape2) |
Quantile value/s using the inverse of the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
x <- qBrXII(u = 0.99, para = c(1, 10, 0.8)) x <- qBrXII(RP = 100, para = c(1, 10, 0.8))x <- qBrXII(u = 0.99, para = c(1, 10, 0.8)) x <- qBrXII(RP = 100, para = c(1, 10, 0.8))
Quantile distribution function of Gamma distribution
qgam(u = NULL, RP = 1/(1 - u), para)qgam(u = NULL, RP = 1/(1 - u), para)
u |
non-exceedance probability |
RP |
Return Period "don't use in case u is used" |
para |
parameters as c(shape, scale) |
Quantile value/s using the inverse of the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
x <- qgam(u = 0.99, para = c(0.1, 0.2)) x <- qgam(RP = 100, para = c(0.1, 0.2))x <- qgam(u = 0.99, para = c(0.1, 0.2)) x <- qgam(RP = 100, para = c(0.1, 0.2))
Quantile distribution function of GEV distribution
qgev(u = NULL, RP = 1/(1 - u), para)qgev(u = NULL, RP = 1/(1 - u), para)
u |
non-exceedance probability |
RP |
Return Period "don't use in case u is used" |
para |
parameters as c(location, scale, shape) |
Quantile value/s using the inverse of the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
x <- qgev(u = 0.99, para = c(10, 1, 1)) x <- qgev(RP = 100, para = c(10, 1, 1))x <- qgev(u = 0.99, para = c(10, 1, 1)) x <- qgev(RP = 100, para = c(10, 1, 1))
Quantile distribution function of the Generalized Gamma (GG) distribution
qGG(u = NULL, RP = 1/(1 - u), para)qGG(u = NULL, RP = 1/(1 - u), para)
u |
non-exceedance probability |
RP |
Return Period "don't use in case u is used" |
para |
parameters as c(scale, shape1, shape2) |
Quantile value/s using the inverse of the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
x <- qGG(u = 0.99, para = c(10, 0.25, 0.5)) x <- qGG(RP = 100, para = c(10, 0.25, 0.5))x <- qGG(u = 0.99, para = c(10, 0.25, 0.5)) x <- qGG(RP = 100, para = c(10, 0.25, 0.5))
Quantile distribution function of Generalized Logistic Distribution
qglo(u = NULL, RP = 1/(1 - u), para)qglo(u = NULL, RP = 1/(1 - u), para)
u |
non-exceedance probability |
RP |
Return Period "don't use in case u is used" |
para |
parameters as c(location, scale, shape) |
Quantile value/s using the inverse of the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
x <- qglo(u = 0.99, para = c(10, 0.1, 0.2)) x <- qglo(RP = 100, para = c(10, 0.1, 0.2))x <- qglo(u = 0.99, para = c(10, 0.1, 0.2)) x <- qglo(RP = 100, para = c(10, 0.1, 0.2))
Quantile distribution function of Generalized normal Distribution
qgno(u = NULL, RP = 1/(1 - u), para)qgno(u = NULL, RP = 1/(1 - u), para)
u |
non-exceedance probability |
RP |
Return Period "don't use in case u is used" |
para |
parameters as c(location, scale, shape) |
Quantile value/s using the inverse of the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
x <- qgno(u = 0.99, para = c(10, 0.1, 0.2)) x <- qgno(RP = 100, para = c(10, 0.1, 0.2))x <- qgno(u = 0.99, para = c(10, 0.1, 0.2)) x <- qgno(RP = 100, para = c(10, 0.1, 0.2))
Quantile distribution function of Generalized Pareto Distribution
qgpa(u = NULL, RP = 1/(1 - u), para)qgpa(u = NULL, RP = 1/(1 - u), para)
u |
non-exceedance probability |
RP |
Return Period "don't use in case u is used" |
para |
parameters as c(location, scale, shape) |
Quantile value/s using the inverse of the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
x <- qgpa(u = 0.99, para = c(10, 0.1, 0.2)) x <- qgpa(RP = 100, para = c(10, 0.1, 0.2))x <- qgpa(u = 0.99, para = c(10, 0.1, 0.2)) x <- qgpa(RP = 100, para = c(10, 0.1, 0.2))
Quantile distribution function of Lognormal-3 Distribution
qln3(u = NULL, RP = 1/(1 - u), para)qln3(u = NULL, RP = 1/(1 - u), para)
u |
non-exceedance probability |
RP |
Return Period "don't use in case u is used" |
para |
parameters as c(zeta, mu, sigma) that is c(lower bound, mean on log scale, standard deviation on log scale). |
Quantile value/s using the inverse of the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
x <- qln3(u = 0.99, para = c(0, 0, 1)) x <- qln3(RP = 100, para = c(0, 0, 1))x <- qln3(u = 0.99, para = c(0, 0, 1)) x <- qln3(RP = 100, para = c(0, 0, 1))
Quantile distribution function of Normal Distribution
qnor(u = NULL, RP = 1/(1 - u), para)qnor(u = NULL, RP = 1/(1 - u), para)
u |
non-exceedance probability |
RP |
Return Period "don't use in case u is used" |
para |
parameters as c(location, scale) |
Quantile value/s using the inverse of the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
x <- qnor(u = 0.99, para = c(10, 0.1)) x <- qnor(RP = 100, para = c(10, 0.1))x <- qnor(u = 0.99, para = c(10, 0.1)) x <- qnor(RP = 100, para = c(10, 0.1))
Quantile distribution function of Pearson type-3 Distribution
qpe3(u = NULL, RP = 1/(1 - u), para)qpe3(u = NULL, RP = 1/(1 - u), para)
u |
non-exceedance probability |
RP |
Return Period "don't use in case u is used" |
para |
parameters as c(mu, sigma, gamma) that is c(location, scale, shape). |
Quantile value/s using the inverse of the cumulative distribution function.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
x <- qpe3(u = 0.99, para = c(1, 1, 0)) x <- qpe3(RP = 100, para = c(1, 1, 0))x <- qpe3(u = 0.99, para = c(1, 1, 0)) x <- qpe3(RP = 100, para = c(1, 1, 0))
Return period function of BrIII distribution
tBrIII(x, para = c(1, 2, 0.5))tBrIII(x, para = c(1, 2, 0.5))
x |
quantile/s |
para |
parameters as c(scale, shape1, shape2) |
Return Period/s corresponding to quantile/s.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
RP <- tBrIII(x = 108.4992, para = c(10, 0.25, 0.5))RP <- tBrIII(x = 108.4992, para = c(10, 0.25, 0.5))
Return period function of BrXII distribution
tBrXII(x, para = c(1, 2, 0.5))tBrXII(x, para = c(1, 2, 0.5))
x |
quantile/s |
para |
parameters as c(scale, shape1, shape2) |
Return Period/s corresponding to quantile/s.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
RP <- tBrXII(x = 108.4992, para = c(10, 0.25, 0.5))RP <- tBrXII(x = 108.4992, para = c(10, 0.25, 0.5))
Return period function of Gamma distribution
tgam(x, para = c(1.5, 1))tgam(x, para = c(1.5, 1))
x |
quantile/s |
para |
parameters as c(shape, scale) |
Return Period/s corresponding to quantile/s.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
RP <- tgam(x = 0.1, para = c(0.1, 0.2))RP <- tgam(x = 0.1, para = c(0.1, 0.2))
Return period function of GEV distribution
tgev(x, para)tgev(x, para)
x |
quantile/s |
para |
parameters as c(location, scale, shape) |
Return Period/s corresponding to quantile/s.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
RP <- tgev(x = 108.4992, para = c(10, 1, 1))RP <- tgev(x = 108.4992, para = c(10, 1, 1))
Return period function of Generalized Gamma distribution
tGG(x, para = c(10, 0.25, 0.5))tGG(x, para = c(10, 0.25, 0.5))
x |
quantile/s |
para |
parameters as c(scale, shape1, shape2) |
Return Period/s corresponding to quantile/s.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
RP <- tGG(x = 108.4992, para = c(10, 0.25, 0.5))RP <- tGG(x = 108.4992, para = c(10, 0.25, 0.5))
Return period function of Generalized Logistic distribution
tglo(x, para = c(10, 1.5, 1))tglo(x, para = c(10, 1.5, 1))
x |
quantile/s |
para |
parameters as c(location, scale, shape) |
Return Period/s corresponding to quantile/s.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
RP <- tglo(x = 0.1, para = c(10, 0.1, 0.2))RP <- tglo(x = 0.1, para = c(10, 0.1, 0.2))
Return period function of Generalized Normal distribution
tgno(x, para = c(10, 1.5, 1))tgno(x, para = c(10, 1.5, 1))
x |
quantile/s |
para |
parameters as c(location, scale, shape) |
Return Period/s corresponding to quantile/s.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
RP <- tgno(x = 10.1, para = c(10, 0.1, 0.2))RP <- tgno(x = 10.1, para = c(10, 0.1, 0.2))
Return period function of Generalized Pareto distribution
tgpa(x, para = c(1, 1, 1))tgpa(x, para = c(1, 1, 1))
x |
quantile/s |
para |
parameters as c(location, scale, shape) |
Return Period/s corresponding to quantile/s.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
RP <- tgpa(x = 1.2, para = c(1, 2, 0.5))RP <- tgpa(x = 1.2, para = c(1, 2, 0.5))
Return period function of Lognormal-3 distribution
tln3(x, para = c(0, 0, 1))tln3(x, para = c(0, 0, 1))
x |
quantile/s |
para |
parameters as c(zeta, mu, sigma) that is c(lower bound, mean on log scale, standard deviation on log scale). |
Return Period/s corresponding to quantile/s.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
RP <- tln3(x = 12, para = c(0, 0, 1))RP <- tln3(x = 12, para = c(0, 0, 1))
Return period function of Noramal distribution
tnor(x, para = c(10, 1.5))tnor(x, para = c(10, 1.5))
x |
quantile/s |
para |
parameters as c(location, scale) |
Return Period/s corresponding to quantile/s.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
RP <- tnor(x = 11, para = c(10, 1.5))RP <- tnor(x = 11, para = c(10, 1.5))
Return period function of Pearson type-3 distribution
tpe3(x, para = c(10, 1, 1.5))tpe3(x, para = c(10, 1, 1.5))
x |
quantile/s |
para |
parameters as c(mu, sigma, gamma) that are c(location, scale, shape). |
Return Period/s corresponding to quantile/s.
Mohanad Zaghloul [aut, cre], Simon Michael Papalexiou [aut, ths], Amin Elshorbagy [aut, ths]
RP <- tpe3(x = 12, para = c(10, 1, 1.5))RP <- tpe3(x = 12, para = c(10, 1, 1.5))