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A New Modified Alpha Power Weibull Distribution: Properties, Parameter Estimation and Application


A new lifetime distribution called alpha power modified Weibull (APMW) distribution based on the alpha power transformation method has been studied. Various statistical properties of the newly developed distribution including quantiles, moments, stress-strength parameter, Bonferroni and Lorentz curve, residual and reversed residual lifetime function, stress-strength parameter, entropy and order statistics have been obtained. Percentage points of the APMW distribution for different values of the parameters have been obtained. The method of maximum likelihood estimation (MLE) has been used for estimating the parameters. A simulation study has been performed to evaluate the behaviour of the MLEs in terms of the sample size n and revealed that as the value of the sample size increases the value of the mean square error decreases showing the reliability of the estimators. The efficiency and flexibility of the new distribution are illustrated by analysing three real-life data sets. In each case, the APMW distribution provides a better fit indicating that the APMW distribution is a justifiable choice for fitting the considered data sets.

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Availability of data and materials

The study materials and the related data set mentioned in this article are from secondary sources. The authors confirm that the data supporting the findings of this study are available in Aldeni et al. (2017), Proschan (1963) and Kosznik-Biernacka (2018).

Code availability

R Programming Software.


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We would like to extend our sincere gratitude to the reviewers for their valuable comments and suggestions. It has greatly improved the manuscript.


No funds, grants, or other support was received for this study.

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This work was carried out in collaboration among the authors. SC, designed the study, performed the statistical analysis and wrote the first draft of the manuscript. BD, managed the literature searches. All authors have contributed to the studies, conception and design which immensely help in the development of this article in all stages of the article formation.

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Correspondence to Bhanita Das.

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Chettri, S., Das, B. & Chakraborty, S. A New Modified Alpha Power Weibull Distribution: Properties, Parameter Estimation and Application. J Indian Soc Probab Stat 22, 417–449 (2021).

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  • Alpha power modified Weibull distribution
  • Moment
  • Quantile
  • Stress-strength reliability
  • Entropy
  • Parameter estimation
  • Simulation