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AKHTAR NAZIMA, BHAT AJAZAHMAD. PRANAV-POWER SERIES DISTRIBUTION: PROPERTIES AND APPLICATIONS TO SURVIVAL AND WAITING TIME DATA. J Sci Arts 2023. [DOI: 10.46939/j.sci.arts-23.1-a08] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/29/2023]
Abstract
This research article presents a new Pranav power series class of distributions which is obtained by compounding one parameter Pranav and power series distributions. Various special cases of the new model have been unfolded. Numerous statistical properties of the proposed model are investigated including closed-form expressions for the density function, cumulative distribution function, survival function, hazard rate function, the moments of order statistics and MLEs. Finally, the flexibility and potentiality of the PPS distribution has been demonstrated by means of two real life data sets.
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Alghamdi SM, Shrahili M, Hassan AS, Mohamed RE, Elbatal I, Elgarhy M. Analysis of Milk Production and Failure Data: Using Unit Exponentiated Half Logistic Power Series Class of Distributions. Symmetry (Basel) 2023; 15:714. [DOI: 10.3390/sym15030714] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/18/2023] Open
Abstract
The unit exponentiated half logistic power series (UEHLPS), a family of compound distributions with bounded support, is introduced in this study. This family is produced by compounding the unit exponentiated half logistic and power series distributions. In the UEHLPS class, some interesting compound distributions can be found. We find formulas for the moments, density and distribution functions, limiting behavior, and other UEHLPS properties. Five well-known estimating approaches are used to estimate the parameters of one sub-model, and a simulation study is created. The simulated results show that the maximum product of spacing estimates had lower accuracy measure values than the other estimates. Ultimately, three real data sets from various scientific areas are used to analyze the performance of the new class.
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Ghazal MGM, Radwan HMM. A reduced distribution of the modified Weibull distribution and its applications to medical and engineering data. Math Biosci Eng 2022; 19:13193-13213. [PMID: 36654042 DOI: 10.3934/mbe.2022617] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
In this work, we suggest a reduced distribution with two parameters of the modified Weibull distribution to avoid some estimation difficulties. The hazard rate function of the reduced distribution exhibits decreasing, increasing or bathtub shape. The suggested reduced distribution can be applied to many problems of modelling lifetime data. Some statistical properties of the proposed distribution have been discussed. The maximum likelihood is employed to estimate the model parameters. The Fisher information matrix is derived and then applied to construct confidence intervals for parameters. A simulation is conducted to illustrate the performance of maximum likelihood estimation. Four sets of real data are tested to prove the proposed distribution advantages. According to the statistical criteria, the proposed distribution fits the tested data better than some well-known two-and three-parameter distributions.
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Affiliation(s)
- M G M Ghazal
- Department of Mathematics, Faculty of Science, Minia University, Minia, Egypt
- Department of Mathematics, University of Technology and Applied Sciences-Al Rustaq, 329-Rustaq, Sultanate of Oman
| | - H M M Radwan
- Department of Mathematics, Faculty of Science, Minia University, Minia, Egypt
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Muhammad M, Bantan RAR, Liu L, Chesneau C, Tahir MH, Jamal F, Elgarhy M. A New Extended Cosine—G Distributions for Lifetime Studies. Mathematics 2021; 9:2758. [DOI: 10.3390/math9212758] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this article, we introduce a new extended cosine family of distributions. Some important mathematical and statistical properties are studied, including asymptotic results, a quantile function, series representation of the cumulative distribution and probability density functions, moments, moments of residual life, reliability parameter, and order statistics. Three special members of the family are proposed and discussed, namely, the extended cosine Weibull, extended cosine power, and extended cosine generalized half-logistic distributions. Maximum likelihood, least-square, percentile, and Bayes methods are considered for parameter estimation. Simulation studies are used to assess these methods and show their satisfactory performance. The stress–strength reliability underlying the extended cosine Weibull distribution is discussed. In particular, the stress–strength reliability parameter is estimated via a Bayes method using gamma prior under the square error loss, absolute error loss, maximum a posteriori, general entropy loss, and linear exponential loss functions. In the end, three real applications of the findings are provided for illustration; one of them concerns stress–strength data analyzed by the extended cosine Weibull distribution.
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Shakhatreh MK, Dey S, Kumar D. Inverse Lindley power series distributions: a new compounding family and regression model with censored data. J Appl Stat 2021; 49:3451-3476. [DOI: 10.1080/02664763.2021.1951683] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Mohammed K. Shakhatreh
- Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan
| | - Sanku Dey
- Department of Statistics, St. Anthony's College, Shillong, India
| | - Devendra Kumar
- Department of Statistics, Central University of Haryana, Mahendergarh, India
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Rivera PA, Calderín-ojeda E, Gallardo DI, Gómez HW. A Compound Class of the Inverse Gamma and Power Series Distributions. Symmetry (Basel) 2021; 13:1328. [DOI: 10.3390/sym13081328] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
In this paper, the inverse gamma power series (IGPS) class of distributions asymmetric is introduced. This family is obtained by compounding inverse gamma and power series distributions. We present the density, survival and hazard functions, moments and the order statistics of the IGPS. Estimation is first discussed by means of the quantile method. Then, an EM algorithm is implemented to compute the maximum likelihood estimates of the parameters. Moreover, a simulation study is carried out to examine the effectiveness of these estimates. Finally, the performance of the new class is analyzed by means of two asymmetric real data sets.
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Shoaee S, Khorram E. Survival analysis for a new compounded bivariate failure time distribution in shock and competing risk models via an EM algorithm. COMMUN STAT-THEOR M 2020. [DOI: 10.1080/03610926.2019.1614193] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Shirin Shoaee
- Department of Actuarial Science, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
| | - Esmaile Khorram
- Department of Statistics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
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Aldahlan MA, Jamal F, Chesneau C, Elbatal I, Elgarhy M. Exponentiated power generalized Weibull power series family of distributions: Properties, estimation and applications. PLoS One 2020; 15:e0230004. [PMID: 32196523 PMCID: PMC7083325 DOI: 10.1371/journal.pone.0230004] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2020] [Accepted: 02/18/2020] [Indexed: 11/19/2022] Open
Abstract
In this paper, we introduce the exponentiated power generalized Weibull power series (EPGWPS) family of distributions, obtained by compounding the exponentiated power generalized Weibull and power series distributions. By construction, the new family contains a myriad of new flexible lifetime distributions having strong physical interpretations (lifetime system, biological studies…). We discuss the characteristics and properties of the EPGWPS family, including its probability density and hazard rate functions, quantiles, moments, incomplete moments, skewness and kurtosis. The main vocation of the EPGWPS family remains to be applied in a statistical setting, and data analysis in particular. In this regard, we explore the estimation of the model parameters by the maximum likelihood method, with accuracy supported by a detailed simulation study. Then, we apply it to two practical data sets, showing the applicability and competitiveness of the EPGWPS models in comparison to some other well-reputed models.
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Affiliation(s)
- Maha A Aldahlan
- Department of Statistics, University of Jeddah, College of Science, Jeddah, Saudi Arabia
| | - Farrukh Jamal
- Department of Statistics, Govt. S.A Postgraduate College Dera Nawab Sahib, Bahawalpur, Punjab, Pakistan
| | | | - Ibrahim Elbatal
- Department of Mathematics and Statistics, College of Science Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia
- Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt
| | - Mohammed Elgarhy
- Valley High Institute for Management Finance and Information Systems, Obour, Qaliubia, Egypt
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Abstract
Mixed models are useful tools for analyzing clustered and longitudinal data. These models assume that random effects are normally distributed. However, this may be unrealistic or restrictive when representing information of the data. Several papers have been published to quantify the impacts of misspecification of the shape of the random effects in mixed models. Notably, these studies primarily concentrated their efforts on models with response variables that have normal, logistic and Poisson distributions, and the results were not conclusive. As such, we investigated the misspecification of the shape of the random effects in a Weibull regression mixed model with random intercepts in the two parameters of the Weibull distribution. Through an extensive simulation study considering six random effect distributions and assuming normality for the random effects in the estimation procedure, we found an impact of misspecification on the estimations of the fixed effects associated with the second parameter σ of the Weibull distribution. Additionally, the variance components of the model were also affected by the misspecification.
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Affiliation(s)
| | - Seyyed Fazel Bagheri
- Department of Mathematics, College of Basic Science, Yadegar-e-Imam Khomeini (RAH) Branch, Islamic Azad University, Tehran, Iran
| | - Mohammad Alizadeh
- Department of Mathematical Sciences, University of Mazandaran, Mazandaran, Iran
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