New Generalization of Length Biased Exponential Distribution with Applications

Abstract

In this paper, a compound continuous distribution (i.e. Exponentiated length biased exponential (E-LBE) distribution) is given. Also, the statistical properties of the proposed distribution are examined, and the parameters are obtained by maximum likelihood estimation method. The flexibility, adequacy, and superiority of the proposed model were investigated by means of applications to dataset. The result indicates that the E-LBE distribution outperformed the competing distributions considered.

The Marshall-olkin Inverse Lomax Distribution (MO-ILD) with Application on Cancer Stem Cell

“…The weaknesses of the conventional measure of kurtosis are well known. Kenney and Keeping [13] gives the Bowely Skewness based on quantiles as;…”

“…Let , … denote a random sample from the densities of a Marshall Olkin inverse Lomax distribution as given in equation (12) and (13) respectively. Then the probability density function : ( ) of the j th order statistics of the MO-ILD is given by;…”

“…In this section, the unknown parameter of the Marshall Olkin inverse Lomax distribution based on a complete sample is estimated using maximum estimation techniques. Let , … indicate a random sample of the complete MO-ILD data, and then the sample's likelihood function is given as[12][13][14][15][16][17];The log likelihood function may be expressed as; ln ( ; , ) = [ln + ln + ln ] − 2 ∑ ln − (1 + ) ∑ ln 1 derivative with respect to , ,, and fixing the outcome to zero, we have;By solving the above derivatives iteratively, we obtain the parameter estimate of the Marshall Olkin inverse Lomax distribution…”

Useful Generalization of the Inverse Lomax Distribution: Statistical Properties and Application to Lifetime Data

“…The dataset obtained from Smith and Naylor [13][14][15][16] represents the strengths of 1.5 cm glass fibres, measured at the National Physi-…”

Statistical modelling for the Covid-19 mortality rate in the Kingdom of Saudi Arabia

“…writers conducted research and generated novel expansions and generalisations of the LBE distribution, such as the Marshall-Olkin LBE distribution that was prepared by ul Haq et al [43] , the inverted LBE that was introduced by Almutiry et al [5] , the Extended Marshall-Olkin LBE distribution, and so on. Elbatal et al [6] , Weibull LBE distribution provided by Ekhosuehi et al [7] , and novel generalisation of LBE distribution presented by Maxwell et al mention [8] …”