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The paper deals with the introduction of new generalized model i.e., Rayleigh Lomax distribution. In this manuscript, a comprehensive description of the various structural properties of the new proposed model including explicit expressions for moments, quantile function, generating functions and Renyi entropy have been given. The parameters of the newly developed distribution have been estimated using the technique of maximum likelihood estimation. Also, the generalized model has been compared with different models for illustration and best fit.

From table 5.1 and 5.2, it is clearly evident that the posterior variance of gamma prior is less than the other priors under both the approximation techniques especially when the value of both the hyper parameters a1 and b1 is taken as 2. Further, it is also noted that the values of normal approximation are less than the T-K approximation for all the three data sets.

Dagum distribution is a statistical distribution used closely for fitting income and wealth distributions. This distribution has wide application in fields like reliability theory survival analysis, actuarial sciences, and meteorological data. In this article, we obtained Bayes estimators for the shape parameter of Dagum distribution using approximation techniques like normal and T-K approximations. Moreover different informative priors have been considered and a simulation study and three real data sets have been considered to study the efficiency of obtained results.

This manuscript considers the transmuted model of the Exponentiated Inverse Weibull distribution. A comprehensive description of the mathematical properties of the proposed model is given in this article. The various properties which include reliability analysis, moments, quantile function, median, moment generating function, characteristic function and order statistics have been discussed in the paper. The method of maximum likelihood estimation has been used for estimating the parameters of the newly proposed distribution. The usefulness of the newly developed model over its sub models for better fitting is illustrated both by the simulated as well as real life data sets.