Year: 2026
Type: article
Abstract: Aim: The aim of the paper is to propose one parameter modified Uma distribution which has the same one parameter as the parameter of the Uma distribution and provide better fit than the Uma distribution. Method: The stochastic character of lifetime data makes it difficult for statisticians to find an appropriate distribution for lifetime data modeling and analysis. In this paper, modified Uma distribution, a modified form of Uma distribution has been proposed where Uma distribution failed to provide better fit. The method used to propose modified Uma distribution is the convex combination approach of deriving new distribution. The convex combination approach of deriving distribution is very popular and several distributions have been derived using this approach in statistics literature. Even Uma distribution has been derived using convex combination approach. Although both Uma distribution and the modified Uma distribution have been derived using convex combination approach, but the proportions of the convex combination are different in both distributions and it is due to proportion, modified Uma distribution provides better fit than the Uma distribution. Results/Findings: Various descriptive moments based measures including coefficient of variation, coefficient of skewness, coefficient of Kurtosis and index of dispersion of the modified Uma distribution have been derived and their natures have also been studied graphically. The comparative study of the index of dispersion of modified Uma distribution with other one parameter lifetime distributions has been present. The statistical properties including deviation from mean and median, Bonferroni and Lorenz curve and order statistics of Uma distribution have been discussed. The reliability properties including stress-strength reliability and Renyi entropy measure has been studied. The parameter estimation using method of moments and the method of maximum likelihood have been discussed. The simulation study to know the consistency of maximum likelihood estimator has been presented. Conclusion: The modified Uma distribution has been fitted to a number of lifetime datasets to test its superiority over other one parameter lifetime distributions. But the goodness of fit of modified Uma distribution has been presented here with three datasets and the goodness of fit of modified Uma distribution has been compared with several one parameter lifetime distributions including Uma, Sujatha, Shanker, Akash, Lindley and exponential distributions and found that the proposed modified Uma distribution provides the best fit.
DOI: 10.66721/rzywan13
Institutions: Assam University, University of Delhi
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7165556354