Distribution.df: Data Frame Summarizing Available Probability Distributions and
Estimation Methods
Description
Data frame summarizing information about available probability
distributions in Rand the EnvStats package, and which
distributions have associated functions for estimating distribution
parameters.source
The EnvStats package.Details
The table below summarizes the probability distributions available in
Rand EnvStats. For each distribution, there are four
associated functions for computing density values, percentiles, quantiles,
and random numbers. The form of the names of these functions are
dabb, pabb, qabb, and
rabb, where abb is the abbreviated name of the
distribution (see table below). These functions are described in the
help file with the name of the distribution (see the first column of the
table below). For example, the help file for Beta describes the
behavior of dbeta, pbeta, qbeta,
and rbeta.
For most distributions, there is also an associated function for
estimating the distribution parameters, and the form of the names of
these functions is eabb, where abb is the
abbreviated name of the distribution (see table below). All of these
functions are listed in the help file
Estimating Distribution Parameters. For example,
the function ebeta estimates the shape parameters of a
Beta distribution based on a random sample of observations from
this distribution.
For some distributions, there are functions to estimate distribution
parameters based on Type I censored data. The form of the names of
these functions is eabbSinglyCensored for
singly censored data and eabbMultiplyCensored for
multiply censored data. All of these functions are listed under the heading
Estimating Distribution Parameters in the help file
Censored Data.
Table 1a. Available Distributions: Name, Abbreviation, Type, and Range
llll{
Name Abbreviation Type Range
Beta beta Continuous $[0, 1]$
Binomial binom Finite $[0, size]$
Discrete (integer)
Cauchy cauchy Continuous $(-\infty, \infty)$
Chi chi Continuous $[0, \infty)$
Chi-square chisq Continuous $[0, \infty)$
Exponential exp Continuous $[0, \infty)$
Extreme evd Continuous $(-\infty, \infty)$
Value
F f Continuous $[0, \infty)$
Gamma gamma Continuous $[0, \infty)$
Gamma gammaAlt Continuous $[0, \infty)$
(Alternative)
Generalized gevd Continuous $(-\infty, \infty)$
Extreme for $shape = 0$
Value
$(-\infty, location + \frac{scale}{shape}]$
for $shape > 0$
$[location + \frac{scale}{shape}, \infty)$
for $shape < 0$
Geometric geom Discrete $[0, \infty)$
(integer)
Hypergeometric hyper Finite $[0, min(k,m)]$
Discrete (integer)
Logistic logis Continuous $(-\infty, \infty)$
Lognormal lnorm Continuous $[0, \infty)$
Lognormal lnormAlt Continuous $[0, \infty)$
(Alternative)
Lognormal lnormMix Continuous $[0, \infty)$
Mixture
Lognormal lnormMixAlt Continuous $[0, \infty)$
Mixture
(Alternative)
Three- lnorm3 Continuous $[threshold, \infty)$
Parameter
Lognormal
Truncated lnormTrunc Continuous $[min, max]$
Lognormal
Truncated lnormTruncAlt Continuous $[min, max]$
Lognormal
(Alternative)
Negative nbinom Discrete $[0, \infty)$
Binomial (integer)
Normal norm Continuous $(-\infty, \infty)$
Normal normMix Continuous $(-\infty, \infty)$
Mixture
Truncated normTrunc Continuous $[min, max]$
Normal
Pareto pareto Continuous $[location, \infty)$
Poisson pois Discrete $[0, \infty)$
(integer)
Student's t t Continuous $(-\infty, \infty)$
Triangular tri Continuous $[min, max]$
Uniform unif Continuous $[min, max]$
Weibull weibull Continuous $[0, \infty)$
Wilcoxon wilcox Finite $[0, m n]$
Rank Sum Discrete (integer)
Zero-Modified zmlnorm Mixed $[0, \infty)$
Lognormal
(Delta)
Zero-Modified zmlnormAlt Mixed $[0, \infty)$
Lognormal
(Delta)
(Alternative)
Zero-Modified zmnorm Mixed $(-\infty, \infty)$
Normal
}
Table 1b. Available Distributions: Name, Parameters, Parameter Default Values, Parameter Ranges, Estimation Method(s)
lllll{
Default Parameter Estimation
Name Parameter(s) Value(s) Range(s) Method(s)
Beta shape1 $(0, \infty)$ mle, mme, mmue
shape2 $(0, \infty)$
ncp 0 $(0, \infty)$
Binomial size $[0, \infty)$ mle/mme/mvue
prob $[0, 1]$
Cauchy location 0 $(-\infty, \infty)$
scale 1 $(0, \infty)$
Chi df $(0, \infty)$
Chi-square df $(0, \infty)$
ncp 0 $(-\infty, \infty)$
Exponential rate 1 $(0, \infty)$ mle/mme
Extreme location 0 $(-\infty, \infty)$ mle, mme, mmue, pwme
Value scale 1 $(0, \infty)$
F df1 $(0, \infty)$
df2 $(0, \infty)$
ncp 0 $(0, \infty)$
Gamma shape $(0, \infty)$ mle, bcmle, mme, mmue
scale 1 $(0, \infty)$
Gamma mean $(0, \infty)$ mle, bcmle, mme, mmue
(Alternative) cv 1 $(0, \infty)$
Generalized location 0 $(-\infty, \infty)$ mle, pwme, tsoe
Extreme scale 1 $(0, \infty)$
Value shape 0 $(-\infty, \infty)$
Geometric prob $(0, 1)$ mle/mme, mvue
Hypergeometric m $[0, \infty)$ mle, mvue
n $[0, \infty)$
k $[1, m+n]$
Logistic location 0 $(-\infty, \infty)$ mle, mme, mmue
scale 1 $(0, \infty)$
Lognormal meanlog 0 $(-\infty, \infty)$ mle/mme, mvue
sdlog 1 $(0, \infty)$
Lognormal mean exp(1/2) $(0, \infty)$ mle, mme, mmue,
(Alternative) cv sqrt(exp(1)-1) $(0, \infty)$ mvue, qmle
Lognormal meanlog1 0 $(-\infty, \infty)$
Mixture sdlog1 1 $(0, \infty)$
meanlog2 0 $(-\infty, \infty)$
sdlog2 1 $(0, \infty)$
p.mix 0.5 $[0, 1]$
Lognormal mean1 exp(1/2) $(0, \infty)$
Mixture cv1 sqrt(exp(1)-1) $(0, \infty)$
(Alternative) mean2 exp(1/2) $(0, \infty)$
cv2 sqrt(exp(1)-1) $(0, \infty)$
p.mix 0.5 $[0, 1]$
Three- meanlog 0 $(-\infty, \infty)$ lmle, mme,
Parameter sdlog 1 $(0, \infty)$ mmue, mmme,
Lognormal threshold 0 $(-\infty, \infty)$ royston.skew,
zero.skew
Truncated meanlog 0 $(-\infty, \infty)$
Lognormal sdlog 1 $(0, \infty)$
min 0 $[0, max)$
max Inf $(min, \infty)$
Truncated mean exp(1/2) $(0, \infty)$
Lognormal cv sqrt(exp(1)-1) $(0, \infty)$
(Alternative) min 0 $[0, max)$
max Inf $(min, \infty)$
Negative size $[1, \infty)$ mle/mme, mvue
Binomial prob $(0, 1]$
mu $(0, \infty)$
Normal mean 0 $(-\infty, \infty)$ mle/mme, mvue
sd 1 $(0, \infty)$
Normal mean1 0 $(-\infty, \infty)$
Mixture sd1 1 $(0, \infty)$
mean2 0 $(-\infty, \infty)$
sd2 1 $(0, \infty)$
p.mix 0.5 $[0, 1]$
Truncated mean 0 $(-\infty, \infty)$
Normal sd 1 $(0, \infty)$
min -Inf $(-\infty, max)$
max Inf $(min, \infty)$
Pareto location $(0, \infty)$ lse, mle
shape 1 $(0, \infty)$
Poisson lambda $(0, \infty)$ mle/mme/mvue
Student's t df $(0, \infty)$
ncp 0 $(-\infty, \infty)$
Triangular min 0 $(-\infty, max)$
max 1 $(min, \infty)$
mode 0.5 $(min, max)$
Uniform min 0 $(-\infty, max)$ mle, mme, mmue
max 1 $(min, \infty)$
Weibull shape $(0, \infty)$ mle, mme, mmue
scale 1 $(0, \infty)$
Wilcoxon m $[1, \infty)$
Rank Sum n $[1, \infty)$
Zero-Modified meanlog 0 $(-\infty, \infty)$ mvue
Lognormal sdlog 1 $(0, \infty)$
(Delta) p.zero 0.5 $[0, 1]$
Zero-Modified mean exp(1/2) $(0, \infty)$ mvue
Lognormal cv sqrt(exp(1)-1) $(0, \infty)$
(Delta) p.zero 0.5 $[0, 1]$
(Alternative)
Zero-Modified mean 0 $(-\infty, \infty)$ mvue
Normal sd 1 $(0, \infty)$
p.zero 0.5 $[0, 1]$
}References
Millard, S.P. (In Preparation). EnvStats: An R Package for
Environmental Statistics. Springer-Verlag, New York.