A New Class of Distributions for Modelling Continuous Positively Skewed Data Sets

Authors

  • Nishant Kumar Srivastava Department of Statistics, Banaras Hindu University, Varanasi, Uttar Pradesh, India
  • Sanjay Kumar Singh Department of Statistics, Banaras Hindu University, Varanasi, Uttar Pradesh, India
  • Vikas Kumar Sharma Department of Statistics, Banaras Hindu University, Varanasi, Uttar Pradesh, India
  • Umesh Singh Department of Statistics, Banaras Hindu University, Varanasi, Uttar Pradesh, India

Keywords:

Generalized probability distribution, moments, quantile function, stress-strength parameter, mean residual life function, Re´nyi entropy, Shannon entropy, maximum likelihood estimation, least squares estimation, maximum product spacing estimation

Abstract

In this paper, we proposed a new class of distributions by introducing a new constant in the existing model. We discuss general properties of the family such as density function, quantile function and hazard rate function. We then discuss a member of the family considering the exponential distribution as baseline distribution. Various properties of the model such as quantile function, moments, moment generating function, order statistics, stress-strength parameter, and mean residual life function are discussed. We also discussed the mean, variance, skewness and kurtosis of the proposed model numerically. The expression for Re´nyi and Shannon entropies are also derived. The different methods of estimation such as maximum likelihood estimation, maximum product spacing and least squares estimates are used for the estimation of the unknown parameters of the proposed distribution. The simulation study is performed to study the behaviour of the estimates based on their mean squared errors. Lastly, we apply our proposed model to two real data sets.

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Published

2024-12-25

How to Cite

Srivastava, N. K. ., Kumar Singh, S. ., Sharma, V. K. ., & Singh, U. . (2024). A New Class of Distributions for Modelling Continuous Positively Skewed Data Sets. Thailand Statistician, 23(1), 1–14. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/257208

Issue

Vol. 23 No. 1 (2025): January

Section

Articles

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