NeuDist (version 1.0.1)

LogisInvWeibull: Logistic Inverse Weibull Distribution

Description

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

Usage

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

Value

• dlogis.inv.weib: numeric vector of (log-)densities

• plogis.inv.weib: numeric vector of probabilities

• qlogis.inv.weib: numeric vector of quantiles

• rlogis.inv.weib: numeric vector of random variates

• hlogis.inv.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 Inverse Weibull distribution is parameterized by the parameters \(\alpha > 0\), \(\beta > 0\), and \(\lambda > 0\).

The Logistic Inverse Weibull distribution has CDF:

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

where \(\alpha\), \(\beta\), and \(\lambda\) are the parameters.

The following functions are included:

• dlogis.inv.weib() — Density function

• plogis.inv.weib() — Distribution function

• qlogis.inv.weib() — Quantile function

• rlogis.inv.weib() — Random generation

• hlogis.inv.weib() — Hazard function

References

Chaudhary,A.K., & Kumar, V.(2020). A Study on Properties and Goodness-of-Fit of The Logistic Inverse Weibull Distribution. Global Journal of Pure and Applied Mathematics(GJPAM), 16(6),871--889. tools:::Rd_expr_doi("10.37622/GJPAM/16.6.2020.871-889")

Examples

x <- seq(0.1, 2.0, 0.2)
dlogis.inv.weib(x, 2.5, 1.5, 0.1)
plogis.inv.weib(x, 2.5, 1.5, 0.1)
qlogis.inv.weib(0.5, 2.5, 1.5, 0.1)
rlogis.inv.weib(10, 2.5, 1.5, 0.1)
hlogis.inv.weib(x, 2.5, 1.5, 0.1)

# Data
x <- stress31
# ML estimates
params = list(alpha=22.20247, beta=0.34507, lambda=3.74216)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = plogis.inv.weib, fit.line=TRUE)

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

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