An extension of the exponential distribution

Abstract

A generalization of the exponential distribution is presented. The generalization always has its mode at zero and yet allows for increasing, decreasing and constant hazard rates. It can be used as an alternative to the gamma, Weibull and exponentiated exponential distributions.A comprehensive account of the mathematical properties of the generalization is presented. A real data example is discussed to illustrate its applicability.

Binomial-exponential 2 Distribution: Different Estimation Methods and Weather Applications

“…Although this is not a standard procedure, yet, without changing this results we will not be able to fit these common distributions. Nadarajah & Haghighi [20] observed that maximum likelihood estimate of the shape parameter is non-unique for the Gamma, Weibull and Generalized exponential distributions if data set consists of zeros and therefore none of these three distributions can fit this kind of data set. On the other hand the BE2 distribution is defined as x ≥ 0, which allow us to use the original values in the presence of zero.…”

The One-Parameter Odd Lindley Exponential Model: Mathematical Properties and Applications

“…This data set was studied by Barlow, Toland and Freeman [13], Andrews and Herzberg [8] and Cooray and Ananda [14]. Using this data set, we fit the TIIOLExp, the exponential (E), the Lindley (L) (Lindley [29]), the generalized exponential (GE) (Gupta and Kundu [19]), the Nadarajah and Haghighi exponential (NH) (Nadarajah and Haghighi [32]), the extended exponential (EE) (Gomez, Bolfarine and Gomez [18]) and the Xgamma (XG) (Sen, Maiti and Chandra [38]) distribution models. The CDFs of the GE, NH, L, EE and XG models are respectively (for x > , α, λ > )…”

Remarks on characterizations of Malinowska and Szynal

“…Here F is the cdf of extension of the exponential distribution (Nadarajah et al, 2011), exp − NH(α, λ), where x ∈ R + ; and α, λ > 0.…”