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Discretized Fréchet–Weibull Distribution: Properties and Application

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Abstract

In this paper a discrete version of Fréchet–Weibull distribution, named as Discretized Fréchet–Weibull distribution has been derived by using the survival function approach of discretization. It has been shown that the distribution is unimodal and right skewed. Depending upon the choice of the parameter, this model can have decreasing and up-side down bathtub shaped hazard rate functions. Various statistical properties of the proposed distribution are obtained. Estimation of parameters by the method of maximum likelihood estimation has been presented. Finally, the proposed model has been applied to five real life datasets from diverse application area namely tensile strength of rubber, \(\text {SO}_2\) content in air pollution, points scored in English League One, the number of deaths per day due to COVID-19 infection in Saudi Arabia and lengths of remission times of leukemia patients. Also, to show its efficacy it is being compared with five other competitive well-known lifetime distributions.

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References

  • Ahmed S, Muhammad A-U-H, Mohamed S (2021) A discrete Ramos-Louzada distribution for asymmetric and over-dispersed data with leptokurtic-shaped: properties. AIMS Math 7(2):1726–1741

    Google Scholar 

  • Almetwally E, Doaa A, Hafez E, Taghreed M, Neveen S, Almongy H (2022) The new discrete distribution with application to COVID-19 Data. Results Phys 32

  • Alzaatreh A, Lee C, Famoye F (2013) A new method for generating families of continuous distributions. Metron 71:63–79

    Article  MathSciNet  MATH  Google Scholar 

  • Chakraborty S (2015) A new discrete distribution related to generalized gamma distribution and its properties. Commun Stat Theory Methods 44(8):1691–1705

    Article  MathSciNet  MATH  Google Scholar 

  • Chakraborty S, Chakravarty D (2012) A new discrete probability distribution with integer support on \((-\infty ,\infty )\). Commun Stat Theory Methods 45(2):492–505

    Article  MathSciNet  MATH  Google Scholar 

  • Chakraborty S, Chakravarty D (2012) Discrete gamma distributions: properties and parameter estimations. Commun Stat Theory Methods 41(18):3301–3324

    Article  MathSciNet  MATH  Google Scholar 

  • Chakraborty S, Chakravarty D, Josmar M, Wesley B (2021) A discrete analog of Gumbel distribution: properties, parameter estimation and application. J Appl Stat 48(4):712–737

    Article  MathSciNet  MATH  Google Scholar 

  • Chakraborty S (2015b) Generating discrete analogues of continuous probability distributions—a survey of methods and constructions. J Stat Distrib Appl 2(6)

  • Deka D, Das B, Baruah BK, Baruah B (2021) Some properties on Fréchet-Weibull distribution with application to real life data. Math Stat 9(1):8–15

    Article  Google Scholar 

  • Elbanna A, Ahmed M, Teamah A-E A M (2020) Fréchet-Weibull distribution with application to earthquakes data sets. Pak J Stat 36(2):135–147

    Google Scholar 

  • Hand D, Daly F, Lunn A, McConway K, Ostrowski E (1994) Handbook of small data sets. Chapman & Hall, London

    Book  MATH  Google Scholar 

  • Ibrahim G, Almetwally E (2021) Discrete Marshall-Olkin Lomax distribution application of COVID-19. Biomed J Sci Tech Res 32(5)

  • Jayakumar K, Babu M (2018) Discrete Weibull geometric distribution and its properties. Commun Stat Theory Methods 47(7):1767–1783

    Article  MathSciNet  MATH  Google Scholar 

  • Jazi MA, Lai CD, Alamatsaz MH (2010) A discrete inverse Weibull distribution and estimation of its parameters. Stat Methodol 7:121–132

    Article  MathSciNet  MATH  Google Scholar 

  • Johnson N, Kemp A, Kotz S (2005) Univariate discrete distributions. Wiley, New York

    Book  MATH  Google Scholar 

  • Khan M, Khalique A, Abouammoh A (1989) On estimating parameters in a discrete Weibull distribution. IEEE Trans Reliab 38:348–350

    Article  MATH  Google Scholar 

  • Krishna H, Pundir P (2009) Discrete Burr and discrete Pareto distributions. Stat Methodol 6:177–188

    Article  MathSciNet  MATH  Google Scholar 

  • Lawless J (2003) Statistical models and methods for lifetime data, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  • Morshedy ME, Altun E, Morshedy MSE (2021) A new statistical approach to model the counts of novel coronavirus cases. Math Sci 1–14

  • Muhammad AUH, Ayesha B, Sharqa H, Abdulaziz SA, Ahmed ZA (2021) The discrete type-II half-logistic exponential distribution with applications to COVID-19 data. Pak. J Stat Oper Res 17(4):921–932

    Article  Google Scholar 

  • Nagy M, Almetwally EM, Gemeay AM, Mohammed HS, Jawa TM, Ahmed NS, Muse AH (2021) The new novel discrete distribution with application on COVID-19 mortality numbers in Kingdom of Saudi Arabia and Latvia. Hindawi, Complexity, 2021

  • Nakagawa T, Osaki S (1975) The discrete Weibull distribution. IEEE Trans Reliab 24(5):300–301

    Article  Google Scholar 

  • Nekoukhou V, Alamatsaz MH, Bidram H (2012) A discrete analog of the generalized exponential distribution. Commun Stat Theory Methods 41(11):2000–2013

    Article  MathSciNet  MATH  Google Scholar 

  • Para BA, Jan TR (2019) On three parameters discrete generalized inverse Weibull distribution: properties and applications. Ann Data Sci 6(3):549–570

    Article  Google Scholar 

  • Roy D (2003) The discrete normal distribution. Commun Stat Theory Methods 32(10):1871–1883

    Article  MathSciNet  MATH  Google Scholar 

  • Roy D (2004) Discrete Rayleigh distribution. IEEE Trans Reliab 53:255–260

    Article  Google Scholar 

  • Stein W, Dattero R (1984) A new discrete Weibull distribution. IEEE Trans Reliab 33:196–197

    Article  MATH  Google Scholar 

  • Steutel F, van Harn K (2004) Infinite divisibility of probability distributions on the real line. Number 259 in Pure and Applied Mathematics. Marcel Dekker

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Authors and Affiliations

  1. Department of Statistics, North-Eastern Hill University, Shillong, Meghalaya, India, 793022

    Diksha Das & Bhanita Das

Authors
  1. Diksha Das
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  2. Bhanita Das
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Contributions

All the authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by DD. BD managed the literature searches. The first draft of the manuscript was written by DD.

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Correspondence to Bhanita Das.

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Das, D., Das, B. Discretized Fréchet–Weibull Distribution: Properties and Application. J Indian Soc Probab Stat 24, 243–282 (2023). https://doi.org/10.1007/s41096-023-00153-w

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