LogisWeib: Logistic-Weibull Distribution

Description

Provides density, distribution, quantile, random generation, and hazard functions for the Logistic-Weibull distribution.

Usage

dlogis.weib(x, alpha, beta, lambda, log = FALSE)
plogis.weib(q, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)
qlogis.weib(p, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)
rlogis.weib(n, alpha, beta, lambda)
hlogis.weib(x, alpha, beta, lambda)

Value

dlogis.weib: numeric vector of (log-)densities
plogis.weib: numeric vector of probabilities
qlogis.weib: numeric vector of quantiles
rlogis.weib: numeric vector of random variates
hlogis.weib: numeric vector of hazard values

Arguments

x, q: numeric vector of quantiles (x, q)
alpha: positive numeric parameter
beta: positive numeric parameter
lambda: positive numeric parameter
log: logical; if TRUE, returns log-density
lower.tail: logical; if TRUE (default), probabilities are $P[X \le x]$ otherwise, $P[X > x]$.
log.p: logical; if TRUE, probabilities are given as log(p)
p: numeric vector of probabilities (0 < p < 1)
n: number of observations (integer > 0)

Details

The Logistic-Weibull distribution is parameterized by the parameters $\alpha > 0$, $\beta > 0$, and $\lambda > 0$.

The Logistic-Weibull distribution has CDF:

$$ F(x; \alpha, \beta, \lambda) = \quad 1 - \frac{1}{{1 + {{\left( {\exp (\lambda {x^\beta }) - 1} \right)} ^\alpha }}}\quad ;\,x \geqslant 0. $$

where $\alpha$, $\beta$, and $\lambda$ are the parameters.

Included functions are:

dlogis.weib() — Density function
plogis.weib() — Distribution function
qlogis.weib() — Quantile function
rlogis.weib() — Random generation
hlogis.weib() — Hazard function

References

Chaudhary,A.K., & Kumar, V.(2021). The Logistic-Weibull distribution with Properties and Applications. IOSR Journal of Mathematics (IOSR-JM), 17(1),Ser.1, 32--41.

Dhungana, G.P., & Kumar, V.(2021). Modified Half Logistic Weibull Distribution with Statistical Properties and Applications. International Journal of Statistics and Reliability Engineering, 8(1), 29-39.

Examples

Run this code

x <- seq(0.1, 10, 0.2)
dlogis.weib(x, 2.0, 0.5, 0.2)
plogis.weib(x, 2.0, 0.5, 0.2)
qlogis.weib(0.5, 2.0, 0.5, 0.2)
rlogis.weib(10, 2.0, 0.5, 0.2)
hlogis.weib(x, 2.0, 0.5, 0.2)

# Data
x <- bladder
# ML estimates
params = list(alpha=2.4165, beta=0.5103, lambda=0.2711)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = plogis.weib, fit.line=TRUE)

#Q-Q (quantile–quantile) plot 
qq.plot(x, params = params, qfun = qlogis.weib, fit.line=TRUE)

# Goodness-of-Fit(GoF) and Model Diagnostics 
out <- gofic(x, params = params,
             dfun = dlogis.weib, pfun=plogis.weib, plot=FALSE)
print.gofic(out)

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