NeuDist (version 1.0.1)

PoissonInvLomax: Poisson Inverse Lomax Distribution

Description

Provides density, distribution, quantile, random generation, and hazard functions for the Poisson Inverse Lomax distribution.

Usage

dpois.inv.lomax(x, alpha, beta, lambda, log = FALSE)
ppois.inv.lomax(q, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)
qpois.inv.lomax(p, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)
rpois.inv.lomax(n, alpha, beta, lambda)
hpois.inv.lomax(x, alpha, beta, lambda)

Value

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

• ppois.inv.lomax: numeric vector of probabilities

• qpois.inv.lomax: numeric vector of quantiles

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

• hpois.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 Poisson Inverse Lomax distribution is parameterized by the parameters \(\alpha > 0\), \(\beta > 0\), and \(\lambda > 0\).

The Poisson Inverse Lomax distribution has CDF:

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

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

The functions available are listed below:

• dpois.inv.lomax() — Density function

• ppois.inv.lomax() — Distribution function

• qpois.inv.lomax() — Quantile function

• rpois.inv.lomax() — Random generation

• hpois.inv.lomax() — Hazard function

References

Joshi, R.K., & Kumar, V. (2021). Poisson Inverted Lomax Distribution: Properties and Applications. International Journal of Research in Engineering and Science (IJRES), 9(1), 48--57.

Chaudhary, A. K., & Kumar, V.(2021). The ArcTan Lomax Distribution with Properties and Applications. International Journal of Scientific Research in Science, Engineering and Technology(IJSRSET), 8(1), 117--125. tools:::Rd_expr_doi("10.32628/IJSRSET218117")

Examples

x <- seq(0.1, 10, 0.2)
dpois.inv.lomax(x, 2.0, 0.5, 0.2)
ppois.inv.lomax(x, 2.0, 0.5, 0.2)
qpois.inv.lomax(0.5, 2.0, 0.5, 0.2)
rpois.inv.lomax(10, 2.0, 0.5, 0.2)
hpois.inv.lomax(x, 2.0, 0.5, 0.2)

# Data
x <- stress
# ML estimates
params = list(alpha=4.1507, beta=5.4091, lambda=80.5762)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = ppois.inv.lomax, fit.line=TRUE)

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

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