E ISSN: 2583-049X
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International Journal of Advanced Multidisciplinary Research and Studies

Volume 3, Issue 1, 2023

Estimating the survival function by Bayes and MLE methods for a proposed new form of Xgamma distribution



Author(s): Mohammed H AL- Sharoot, Karrar R AL-Sayeab

Abstract:

In this research, we have studied a new form of the Xgamma (XG) distribution, resulting from mixing the two distributions exponential with parameter (λ=1/θ), and gamma with the two parameters (3, λ=1/θ), with the substitution of the mixing weights in the mixing equation for the distribution XG, one in place of the other, which produced a new form for which we proposed the name Xgamma3 distribution (XG3D). Then we derive some mathematical properties and some survival properties of the new proposed shape XG3D, we estimate the survival function of the proposed shape by estimating its parameter with two estimation methods (the Standard Bayesian and maximum likelihood estimation methods).

A simulation study was carried out to find out which of the two estimation methods is the best by comparing them by Integrated Mean square Error, which showed that the standard Bayes method is the best.

And using real data (for patients infected with the Covid-19 virus in the city of Najaf, Iraq), the proposed shape was compared with the original form of the XG distribution (some of its mathematical and survival properties were presented and its survival function was estimated using the same methods above) and the comparison was made using the criteria (AIC, AICc, BIC), which concluded that the original form of distribution was better than the proposed form because it achieved the lowest comparative criteria, but the proposed form remains a competitive model.


Keywords: Xgamma Distribution, Xgamma3 Distribution, Survival Function, Standard Bayes Estimation, Maximum Likelihood Estimation

Pages: 368-373

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