NeuDist (version 1.0.1)

LindleyExpPower: Lindley-Exponential Power Distribution

Description

Provides density, distribution, quantile, random generation, and hazard functions for the Lindley-Exponential Power distribution.

Usage

dlind.exp.pow(x, alpha, lambda, theta, log = FALSE)
plind.exp.pow(q, alpha, lambda, theta, lower.tail = TRUE, log.p = FALSE)
qlind.exp.pow(p, alpha, lambda, theta, lower.tail = TRUE, log.p = FALSE)
rlind.exp.pow(n, alpha, lambda, theta)
hlind.exp.pow(x, alpha, lambda, theta)

Value

• dlind.exp.pow: numeric vector of (log-)densities

• plind.exp.pow: numeric vector of probabilities

• qlind.exp.pow: numeric vector of quantiles

• rlind.exp.pow: numeric vector of random variates

• hlind.exp.pow: numeric vector of hazard values

Arguments

x, q

numeric vector of quantiles (x, q)

alpha

positive numeric parameter

lambda

positive numeric parameter

theta

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 Lindley-Exponential Power distribution is parameterized by the parameters \(\alpha > 0\), \(\lambda > 0\), and \(\theta > 0\).

The Lindley-Exponential Power distribution has CDF:

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

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

The following functions are included:

• dlind.exp.pow() — Density function

• plind.exp.pow() — Distribution function

• qlind.exp.pow() — Quantile function

• rlind.exp.pow() — Random generation

• hlind.exp.pow() — Hazard function

References

Joshi, R. K., & Kumar, V. (2020). Lindley exponential power distribution with Properties and Applications. International Journal for Research in Applied Science & Engineering Technology (IJRASET), 8(10), 22--30. tools:::Rd_expr_doi("10.22214/ijraset.2020.31743")

Joshi, R.K., & Kumar, V. (2016). Exponentiated Power Lindley Distribution : A Bayes Study using MCMC Approach. J. Nat. Acad. Math., 30, 80--102.

Examples

x <- seq(1.0, 5, 0.25)
dlind.exp.pow(x, 0.5, 0.2, 1.5)
plind.exp.pow(x, 0.5, 0.2, 1.5)
qlind.exp.pow(0.5, 0.5, 0.2, 1.5)
rlind.exp.pow(10, 0.5, 0.2, 1.5)
hlind.exp.pow(x, 0.5, 0.2, 1.5)

# Data
x <- windshield
# ML estimates
params = list(alpha=0.97722, lambda=0.39461, theta=0.96124)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = plind.exp.pow, fit.line=TRUE)

#Q-Q (quantile–quantile) plot 
qq.plot(x, params = params, qfun = qlind.exp.pow, fit.line=TRUE)

# Goodness-of-Fit(GoF) and Model Diagnostics 
out <- gofic(x, params = params,
             dfun = dlind.exp.pow, pfun=plind.exp.pow, plot=FALSE)
print.gofic(out)