NeuDist (version 1.0.1)

LogisInvLomax: Logistic Inverted Lomax Distribution

Description

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

Usage

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

Value

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

• plogis.inv.lomax: numeric vector of probabilities

• qlogis.inv.lomax: numeric vector of quantiles

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

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

The Logistic Inverted Lomax distribution has CDF:

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

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

The following functions are included:

• dlogis.inv.lomax() — Density function

• plogis.inv.lomax() — Distribution function

• qlogis.inv.lomax() — Quantile function

• rlogis.inv.lomax() — Random generation

• hlogis.inv.lomax() — Hazard function

References

Joshi, R. K., & Kumar, V. (2021). The Logistic Inverse Lomax Distribution with Properties and Applications. International Journal of Mathematics and Computer Research, 9(1), 2169--2177. tools:::Rd_expr_doi("10.47191/ijmcr/v9i1.02")

Lan, Y., & Leemis, L. M. (2008). The Logistic-Exponential Survival Distribution. Naval Research Logistics, 55, 252--264.

Examples

x <- seq(0.1, 10, 0.2)
dlogis.inv.lomax(x, 2.0, 5.0, 0.2)
plogis.inv.lomax(x, 2.0, 5.0, 0.2)
qlogis.inv.lomax(0.5, 2.0, 5.0, 0.2)
rlogis.inv.lomax(10, 2.0, 5.0, 0.2)
hlogis.inv.lomax(x, 2.0, 5.0, 0.2)

# Data
x <- bladder
# ML estimates
params = list(alpha=2.87951, beta=38.51405, lambda=0.35313)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = plogis.inv.lomax, fit.line=TRUE)

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

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