NeuDist (version 1.0.1)

LogisRayleigh: Logistic-Rayleigh Distribution

Description

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

Usage

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

Value

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

• plogis.rayleigh: numeric vector of probabilities

• qlogis.rayleigh: numeric vector of quantiles

• rlogis.rayleigh: numeric vector of random variates

• hlogis.rayleigh: numeric vector of hazard values

Arguments

x, q

numeric vector of quantiles (x, q)

alpha

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-Rayleigh distribution is parameterized by the parameters \(\alpha > 0\) and \(\lambda > 0\).

The Logistic-Rayleigh distribution has CDF:

$$ F(x; \alpha, \lambda) = 1 - \frac{1}{{1 + {{\left( {{e^{(\lambda {x^2}/2)}} - 1} \right)}^\alpha }}} \, ; \quad x \geq 0. $$

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

The following functions are included:

• dlogis.rayleigh() — Density function

• plogis.rayleigh() — Distribution function

• qlogis.rayleigh() — Quantile function

• rlogis.rayleigh() — Random generation

• hlogis.rayleigh() — Hazard function

References

Chaudhary, A.K., & Kumar, V. (2020). The Logistic - Rayleigh Distribution with Properties and Applications. International Journal of Statistics and Applied Mathematics, 5(6), 12--19. tools:::Rd_expr_doi("10.22271/maths.2020.v5.i6a.603")

Examples

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

# Data
x <- conductors
# ML estimates
params = list(alpha=2.6967, lambda=0.0291)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = plogis.rayleigh, fit.line=TRUE)

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

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