Order {DescTools} R Documentation

## Distributions of Order Statistics

### Description

Density function, distribution function and random generation for a selected Order statistic of a given number of independent variables from a specified distribution.

### Usage

dOrder(x, densfun, distnfun, ..., distn, mlen = 1, j = 1,
largest = TRUE, log = FALSE)
pOrder(q, distnfun, ..., distn, mlen = 1, j = 1, largest = TRUE,
lower.tail = TRUE)
rOrder(n, quantfun, ..., distn, mlen = 1, j = 1, largest = TRUE)


### Arguments

 x, q Vector of quantiles. n Number of observations. densfun, distnfun, quantfun Density, distribution and quantile function of the specified distribution. The density function must have a log argument (a simple wrapper can always be constructed to achieve this). ... Parameters of the specified distribution. distn A character string, optionally specified as an alternative to densfun, distnfun and quantfun such that the density, distribution and quantile functions are formed upon the addition of the prefixes d, p and q respectively. mlen The number of independent variables. j The Order statistic, taken as the jth largest (default) or smallest of mlen, according to the value of largest. largest Logical; if TRUE (default) use the jth largest Order statistic, otherwise use the jth smallest. log Logical; if TRUE, the log density is returned. lower.tail Logical; if TRUE (default) probabilities are P[X <= x], otherwise P[X > x].

### Value

dOrder gives the density function, pOrder gives the distribution function and qOrder gives the quantile function of a selected Order statistic from a sample of size mlen, from a specified distibution. rOrder generates random deviates.

### Author(s)

Alec Stephenson <alec_stephenson@hotmail.com>

rExtrVal, rGenExtrVal
dOrder(2:4, dnorm, pnorm, mean = 0.5, sd = 1.2, mlen = 5, j = 2)