estdweibull3: Estimation of parameters In DiscreteWeibull: Discrete Weibull Distributions (Type 1 and 3)

Description

Estimation of the parameters of the type 3 discrete Weibull distribution

Usage

 `1` ```estdweibull3(x, method = "P", eps = 1e-04) ```

Arguments

 `x` the vector of sample values `method` `"ML"` for the maximum likelihood method; `"M"` for the method of moments; `"P"` for the method of proportions `eps` error threshold for the computation of the moments of the distribution

Value

the vector of the estimates of c and β

Author(s)

Alessandro Barbiero

`ddweibull3`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44``` ```# Ex1 x <- c(0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,3,3,4,6) estdweibull3(x, "P") estdweibull3(x, "ML") estdweibull3(x, "M") # Ex 2 n <- 20 c <- 1/3 beta <- 2/3 x <- rdweibull3(n, c, beta) estdweibull3(x, "P") par <- estdweibull3(x, "ML") par -loglikedw3(par, x) par <- estdweibull3(x, "M") par lossdw3(par, x) n <- 50 x <- rdweibull3(n, c, beta) estdweibull3(x, "P") estdweibull3(x, "ML") estdweibull3(x, "M") n <- 100 x <- rdweibull3(n, c, beta) estdweibull3(x, "P") estdweibull3(x, "ML") estdweibull3(x, "M") # Ex 3: a piece of simulation study nSim <- 50 n <- 50 c <- 0.2 beta <- 0.7 par <- matrix(0, nSim, 2) for(i in 1:nSim) { x <- rdweibull3(n, c, beta) par[i,] <- estdweibull3(x, "ML") } op <- par(mfrow = c(1,2)) boxplot(par[,1], xlab=expression(hat(c)[ML])) abline(h = c) boxplot(par[,2], xlab=expression(hat(beta)[ML])) abline(h = beta) op <- par() ```