LogisLomax: Logistic-Lomax Distribution

Description

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

Usage

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

Value

dlogis.lomax: numeric vector of (log-)densities
plogis.lomax: numeric vector of probabilities
qlogis.lomax: numeric vector of quantiles
rlogis.lomax: numeric vector of random variates
hlogis.lomax: 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-Lomax distribution is parameterized by the parameters $\alpha > 0$, $\beta > 0$, and $\lambda > 0$.

The Logistic-Lomax distribution has CDF:

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

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

The following functions are included:

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

References

Chaudhary, A.K., & Kumar, V.(2020). The Logistic Lomax Distribution with Properties and Applications. International Journal of New Technology and Research, 6(12), 74--80. tools:::Rd_expr_doi("10.31871/IJNTR.6.12.21")

Shrestha, S.K., & Kumar, V. (2014). Bayesian Analysis of Extended Lomax Distribution. International Journal of Mathematical Trends and Technology (IJMTT), 7(1), 33--41. tools:::Rd_expr_doi("10.14445/22315373/IJMTT-V7P505")

Examples

Run this code

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

# Data
x <- bladder
# ML estimates
params = list(alpha=1.38027, beta=0.04451, lambda=2.80412)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = plogis.lomax, fit.line=TRUE)

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

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

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