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- Title
A New Lifetime Distribution with Properties, Characterizations, Validation Testing and Different Estimation Methods.
- Authors
Yousof, Haitham M.; Ali, M. Masoom; Aidi, Khaoula; Hamedani, G. G.; Ibrahim, Mohamed
- 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, Cram'er-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 flexibility of the new model. Using the validation approach proposed by Bagdonavicius and Nikulin (2011) for censored data, we propose the construction of modified chi-square goodness-of-fit tests for the new model. Based on the maximum likelihood estimators on initial data, the modified statistics recover the information lost while grouping data and follow chi-square models. All elements of the modified criteria tests are given explicitly. Numerical example from simulated samples and four real data sets have been analyzed to illustrate the feasibility of the modified test.
- Subjects
LEAST squares; MAXIMUM likelihood statistics; GOODNESS-of-fit tests; CENSORING (Statistics); COPULA functions; WEIBULL distribution; NUMERICAL calculations
- Publication
Statistics, Optimization & Information Computing, 2022, Vol 10, Issue 2, p519
- ISSN
2311-004X
- Publication type
Article
- DOI
10.19139/soic-2310-5070-1222