The Length-Biased Weighted Exponentiated Inverted Exponential Distribution: Properties and Estimation

Abstract

This paper introduces the length-biased weighted exponentiated inverted exponential distribution with sub models. The basic statistical properties are derived such as mean, mode, variance, reliability functions, moment generating function, characteristic function and order statistic distribution. Furthermore, maximum likelihood estimators of distribution parameters are obtained under censored Type I. Numerical study is applied. Variance-covariance matrix is obtained and Confidence intervals are calculated. Two real data sets are applied to compare performance of the proposed model with competitive distributions by using some criterions as measures of goodness fit.

A Novel Three-Parameter Nadarajah Haghighi Model: Entropy Measures, Inference, and Applications

“…It is well-documented that the NH model can be extensively investigated in many study domains. Noteworthy studies involving this model include Almetwally and Meraou [27], Korkmaz et al [28], Salama et al [29], Almongy et al [30], Tahir et al [31], Lone et al [32], Shafq et al [33], and Anum Shafiq et al [34]. The cdf and pdf of an NH distribution are formulated, respectively, as G(y) = 1 − e 1−(1+βy) α , y, α, β > 0, (5) and g(y) = αβ(1 + βy) α−1 e 1−(1+βy) α , (6) where α and β represent the shape and scale parameters, respectively.…”