New discrete Ramos–Louzada exponential–type distribution with applications to biological and COVID-19 data

Ahood Abdalrahman Alazwari; Ayşe Metin Karakaş; Fatma Bulut; Eslam Hussam; Muhammad Ahsan-ul-Haq; Samirah Alzubaidi; Amani Alrumayh; M. E. Sobh; Ahood Abdalrahman Alazwari; Ayşe Metin Karakaş; Fatma Bulut; Eslam Hussam; Muhammad Ahsan-ul-Haq; Samirah Alzubaidi; Amani Alrumayh; M. E. Sobh

doi:10.3934/math.20261083

AIMS Mathematics

2026, Volume 11, Issue 8: 27018-27055. doi: 10.3934/math.20261083

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Research article

New discrete Ramos–Louzada exponential–type distribution with applications to biological and COVID-19 data

1.
Department of Mathematics, Faculty of Science, Al-Baha University, Al-Baha, Saudi Arabia
2.
Statistics department, Faculty of Arts and Sciences, Bitlis Eren University, Bitlis
3.
Mathematics department, Faculty of Arts and Sciences, Bitlis Eren University, Bitlis
4.
Department of Accounting, College of Business Administration in Hawtat Bani Tamim, Prince Sattam bin Abdulaziz University, Saudi Arabia
5.
Mathematics department, Faculty of Science, Capital University, Cairo, Egypt
6.
College of Statistical Sciences, University of the Punjab, Lahore, Pakistan
7.
Department of Mathematics, Al-Qunfudah University College, Umm Al-Qura University, Mecca, Saudi Arabia
8.
Department of Mathematics, College of Science, Northern Border University, Arar, Saudi Arabia
9.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt

Received: 07 June 2026 Revised: 31 July 2026 Accepted: 05 August 2026 Published: 27 August 2026
MSC : 62E15, 62F10, 62F15, 62N05

In this study, we introduced a novel discrete probability model, the discrete Ramos–Louzada exponential distribution, obtained by discretizing the survival function of its continuous counterpart. With a flexible two-parameter structure, the model captured diverse behaviors observed in count data. Core distributional properties, including the probability mass function, cumulative distribution function, survival function, hazard rate, and moment-generating function, were derived analytically. Log-concavity and an increasing hazard rate are established, supporting suitability for reliability and lifetime-type counts. Parameters were estimated using the maximum likelihood and Bayesian approaches, and finite-sample performance was evaluated through extensive simulation studies. Practical applicability was illustrated using European corn-borer larvae counts and daily COVID-19 mortality data from South Korea. Comparative goodness-of-fit results against established discrete models demonstrated superior performance, highlighting effectiveness.
- discrete distribution,
- Ramos–Louzada exponential distribution,
- survival discretization,
- parameter estimation,
- COVID-19 data
Citation: Ahood Abdalrahman Alazwari, Ayşe Metin Karakaş, Fatma Bulut, Eslam Hussam, Muhammad Ahsan-ul-Haq, Samirah Alzubaidi, Amani Alrumayh, M. E. Sobh. New discrete Ramos–Louzada exponential–type distribution with applications to biological and COVID-19 data[J]. AIMS Mathematics, 2026, 11(8): 27018-27055. doi: 10.3934/math.20261083

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Abstract

In this study, we introduced a novel discrete probability model, the discrete Ramos–Louzada exponential distribution, obtained by discretizing the survival function of its continuous counterpart. With a flexible two-parameter structure, the model captured diverse behaviors observed in count data. Core distributional properties, including the probability mass function, cumulative distribution function, survival function, hazard rate, and moment-generating function, were derived analytically. Log-concavity and an increasing hazard rate are established, supporting suitability for reliability and lifetime-type counts. Parameters were estimated using the maximum likelihood and Bayesian approaches, and finite-sample performance was evaluated through extensive simulation studies. Practical applicability was illustrated using European corn-borer larvae counts and daily COVID-19 mortality data from South Korea. Comparative goodness-of-fit results against established discrete models demonstrated superior performance, highlighting effectiveness.

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