ddweibull: The type 1 discrete Weibull distribution In DiscreteWeibull: Discrete Weibull Distributions (Type 1 and 3)

Description

Probability mass function, distribution function, quantile function and random generation for the discrete Weibull distribution with parameters q and β

Usage

 ```1 2 3 4``` ```ddweibull(x, q, beta, zero = FALSE) pdweibull(x, q, beta, zero = FALSE) qdweibull(p, q, beta, zero = FALSE) rdweibull(n, q, beta, zero = FALSE) ```

Arguments

 `x` vector of quantiles `p` vector of probabilities `q` first parameter `beta` second parameter `zero` `TRUE`, if the support contains 0; `FALSE` otherwise `n` sample size

Details

The discrete Weibull distribution has probability mass function given by P(X=x;q,β)=q^{(x-1)^{β}}-q^{x^{β}}, x=1,2,3,…, if `zero`=`FALSE`; or P(X=x;q,β)=q^{x^{β}}-q^{(x+1)^{β}}, x=0,1,2,…, if `zero`=`TRUE`. The cumulative distribution function is F(x;q,β)=1-q^{x^{β}} if `zero`=`FALSE`; F(x;q,β)=1-q^{(x+1)^{β}} otherwise

Value

`ddweibull` gives the probability function, `pdweibull` gives the distribution function, `qdweibull` gives the quantile function, and `rdweibull` generates random values.

Author(s)

Alessandro Barbiero

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24``` ```# Ex.1 x <- 1:10 q <- 0.6 beta <- 0.8 ddweibull(x, q, beta) t <- qdweibull(0.99, q, beta) t pdweibull(t, q, beta) # x <- 0:10 ddweibull(x, q, beta, zero=TRUE) t <- qdweibull(0.99, q, beta, zero=TRUE) t pdweibull(t, q, beta, zero=TRUE) # Ex.2 q <- 0.4 beta <- 0.7 n <- 100 x <- rdweibull(n, q, beta) tabulate(x)/sum(tabulate(x)) y <- 1:round(max(x)) # compare with ddweibull(y, q, beta) ```

Example output

```Loading required package: Rsolnp
[1] 0.40000000 0.18909740 0.11866347 0.07967971 0.05550770 0.03961701
[7] 0.02877831 0.02119190 0.01577790 0.01185488
[1] 16
[1] 0.9908525
[1] 0.400000000 0.189097397 0.118663474 0.079679712 0.055507700 0.039617011
[7] 0.028778312 0.021191898 0.015777899 0.011854881 0.008976778
[1] 15
[1] 0.9908525
[1] 0.57 0.18 0.08 0.08 0.02 0.02 0.01 0.00 0.01 0.02 0.01
[1] 0.600000000 0.174293249 0.087229935 0.049386598 0.029894854 0.018908549
[7] 0.012346468 0.008261763 0.005638307 0.003911069 0.002750606
```

DiscreteWeibull documentation built on May 2, 2019, 8:58 a.m.