NeuDist (version 1.0.1)

PoisInvWeib: Poisson Inverse Weibull Distribution

Description

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

Usage

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

Value

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

• ppois.inv.weib: numeric vector of probabilities

• qpois.inv.weib: numeric vector of quantiles

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

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

The Poisson Inverse Weibull distribution has CDF:

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

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

References

Kus, C. (2007). A new lifetime distribution. Computational Statistics and Data Analysis, 51, 4497--4509.

Joshi, R. K., & Kumar, V. (2021). Poisson Inverse Weibull Distribution with Theory and Applications. International Journal of Statistics and Systems, 16(1), 1--16.

Rodrigues, G.C., Louzada, F., & Ramos, P.L.(2018). Poisson–exponential distribution: different methods of estimation. Journal of Applied Statistics, 45(1), 128--144.

Examples

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

# Data
x <- fibers63
# ML estimates
params = list(alpha=5.5146, beta=1.8811, lambda=16.2341)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = ppois.inv.weib, fit.line=TRUE)

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

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