# A New Lifetime Distribution with Properties, Characterizations, Validation Testing and Different Estimation Methods

### Abstract

A new lifetime distribution is proposed and its properties are studied. The new density function has a heavy right skew tails with different shapes. The new failure rate function can be “constant”, “bathtub (U)”, “increasing-constant”, “decreasing-constant”, “upside down” and “upside down-U”. Complexity of the most integrals related to statistical properties is solved and numerically analyzed. Simple type copula is presented. Numerical calculations for analyzing the skewness and kurtosis are presented. Different estimation methods such as the maximum likelihood estimation method, Cramer-von-Mises estimation method, ordinary least square estimation method, weighted least square estimation method, Anderson Darling estimation method, right tail Anderson Darling estimation method and left tail-Anderson Darling estimation method are considered. Numerical simulation studies are performed. An example of environmental real data set is employed to compare the estimation methods. Another example is presented to measure importance and flflexibility of the new model. Using the validation approach proposed by Bagdonavicius and Nikulin (2011) for censored data, we propose the construction of modifified chi-square goodness-of-fifit tests for the new model. Based on the maximum likelihood estimators on initial data, the modifified statistics recover the information lost while grouping data and follow chi-square models. All elements of the modifified criteria tests are given explicitly. Numerical example from simulated samples and four real data sets have been analyzed to illustrate the feasibility of the modifified test.### References

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