Expected values

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Description

First and second order moments for the type 3 discrete Weibull distribution

Usage

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Edweibull3(c, beta, eps = 1e-04)
E2dweibull3(c, beta, eps = 1e-04)

Arguments

c

first parameter

beta

second parameter

eps

error threshold for the numerical computation of the expected value

Details

The expected values are numerically computed considering a truncated support: integer values smaller than or equal to 2F^{-1}(1-eps;c,β)), where F^{-1} is the inverse of the cumulative distribution function (implemented by the function qdweibull3)

Value

the (approximate) expected values of the discrete Weibull distribution: Edweibull3 gives the first order moment, E2dweibull3 the second order moment

Author(s)

Alessandro Barbiero

Examples

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c <- 0.4
beta <- 0.25
Edweibull3(c,beta)
c <- 0.4
beta <- -0.75
Edweibull3(c, beta) # may require too much time
Edweibull3(c, beta, eps=0.001) # try with a smaller eps->worse approximation
c <- rep(0.1, 11)
beta <- (0:10)/10
Edweibull3(c, beta)
c <- rep(0.5, 11)
beta <- (-5:5)/10
Edweibull3(c,beta)
# E2dweibull3
c <- 0.4
beta <- 0.25
E2dweibull3(c, beta)
c <- rep(0.1, 11)
beta <- (0:10)/10
Edweibull3(c, beta)
c <- rep(0.8, 11)
beta <- (-5:5)/11
E2dweibull3(c, beta)