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  • 1 Persian Gulf University, Bushehr, Iran
  • | 2 Fasa University, Fasa, Iran
  • | 3 Marquette University, Milwaukee, USA
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Abstract

In this paper, we introduce a new three-parameter generalized version of the Gompertz model called the odd log-logistic Gompertz (OLLGo) distribution. It includes some well-known lifetime distributions such as Gompertz (Go) and odd log-logistic exponential (OLLE) as special sub-models. This new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a decreasing, increasing and bathtub-shaped failure rate function depending on its parameters. Some mathematical properties of the new distribution, such as closed-form expressions for the density, cumulative distribution, hazard rate function, the kth order moment, moment generating function and the quantile measure are provided. We discuss maximum likelihood estimation of the OLLGo parameters as well as three other estimation methods from one observed sample. The flexibility and usefulness of the new distribution is illustrated by means of application to a real data set.

  • [1]

    Aarset, M. V., How to identify a bathtub hazard rate, IEEE Transactions on Reliability, R-36 (1) (1987), 106108.

  • [2]

    Akinsete, A., Famoye, F. and Lee, C., The beta-Pareto distribution, Statistics, 42 (6) (2008), 547563.

  • [3]

    Bemmaor, A. C. and Glady, N., Modeling purchasing behavior with sudden “death”: A flexible customer lifetime model, Management Science 58 (5) (2012), 10121021.

    • Search Google Scholar
    • Export Citation
  • [4]

    Benkhelifa, L., The Marshall-Olkin extended generalized Gompertz distribution, arXiv preprint arXiv:1603.08242, 2016.

  • [5]

    Brown, K. and Forbes, W., A mathematical model of aging processes, Journal of Gerontology, 29 (1) (1974), 4651.

  • [6]

    Cintra, R. J., Râgo, L. C., Cordeiro, G. M. and Nascimento, A. D. C., Beta generalized normal distribution with an application for SAR image processing, Statistics, 48 (2) (2012), 279294.

    • Search Google Scholar
    • Export Citation
  • [7]

    Cooray, K., Generalization of the Weibull distribution: the odd Weibull family, Statistical Modelling, 6 (3) (2006), 265277.

  • [8]

    Cordeiro, G. M. and Nadarajah, S., Closed-form expressions for moments of a class of beta generalized distributions, Brazilian Journal of Probability and Statistics, 25 (1) (2011), 1433.

    • Search Google Scholar
    • Export Citation
  • [9]

    Cox, D. R. and Hinkley, D. V., Theoretical Statistics, Chapman and Hall, London, 1974.

  • [10]

    Economos, A. C., Rate of aging, rate of dying and the mechanism of mortality, Archives of Gerontology and Geriatrics, 1 (1) (1982), 4651.

    • Search Google Scholar
    • Export Citation
  • [11]

    El-Gohary, A., Alshamrani, A. and Al-Otaibi, A. N., The generalized Gompertz distribution, Applied Mathematical Modelling, 37 (1–2) (2013), 1324.

    • Search Google Scholar
    • Export Citation
  • [12]

    Eugene, N., Lee, C. and Famoye, F., Beta-normal distribution and its applications, Communications in Statistics — Theory and Methods, 31 (4) (2002), 497512.

    • Search Google Scholar
    • Export Citation
  • [13]

    Glänzel, W., A characterization theorem based on truncated moments and its application to some distribution families, Mathematical Statistics and Probability Theory (Bad Tatzmannsdorf, 1986), Vol. B, Reidel, Dordrecht, 1987, 7584.

    • Search Google Scholar
    • Export Citation
  • [14]

    Glänzel, W., Some consequences of a characterization theorem based on truncated moments, Statistics: A Journal of Theoretical and Applied Statistics, 21 (4) (1990), 613618.

    • Search Google Scholar
    • Export Citation
  • [15]

    Gleaton, J. U. and Lynch, J. D., Properties of generalized log-logistic families of lifetime distributions, Journal of Probability and Statistical Science, 4 (1) (2006), 5164.

    • Search Google Scholar
    • Export Citation
  • [16]

    Gleaton, J. U. and Rahman, M. M., Asymptotic properties of MLE's for distributions generated from a 2-parameter Weibull distribution by a generalized log-logistic transformation, Journal of Probability and Statistical Science, 8 (2010), 199214.

    • Search Google Scholar
    • Export Citation
  • [17]

    Gleaton, J. U. and Rahman, M. M., Asymptotic properties of MLE's for distributions generated from a 2-parameter inverse Gaussian distribution by a generalized log-logistic transformation, Journal of Probability and Statistical Science, 12 (2014), 8599.

    • Search Google Scholar
    • Export Citation
  • [18]

    Gradshteyn, I. S. and Ryzhik, I. M., Table of Integrals, Series, and Products, Edited by Alan Jeffrey and Daniel Zwillinger, Academic Press, 7th edition, 2007.

    • Search Google Scholar
    • Export Citation
  • [19]

    Gupta, R. C. and Gupta, R. D., Proportional reversed hazard rate model and its applications, Journal of Statistical Planning and Inference, 137 (11) (2007), 35253536.

    • Search Google Scholar
    • Export Citation
  • [20]

    Gupta, R. D. and Kundu, D., Generalized exponential distributions, Australian & New Zealand Journal of Statistics, 41 (2) (1999), 173188.

    • Search Google Scholar
    • Export Citation
  • [21]

    Hamedani, G. G., On certain generalized gamma convolution distributions II, Technical Report No. 484, 2013, MSCS, Marquette University.

    • Search Google Scholar
    • Export Citation
  • [22]

    Jafari, A. A., Tahmasebi, S. and Alizadeh, M., The Beta-Gompertz Distribution, Revista Colombiana de Estadística, 37 (1) (2014), 139156.

    • Search Google Scholar
    • Export Citation
  • [23]

    Johnson, N. L., Kotz, S. and Balakrishnan, N., Continuous Univariate Distributions, volume 2, John Wiley & Sons, New York, second edition, 1995.

    • Search Google Scholar
    • Export Citation
  • [24]

    Kenney, J. F. and Keeping, E., Mathematics of Statistics, D. Van Nostrand Company, 1962.

  • [25]

    Moors, J. J. A., A quantile alternative for kurtosis, Journal of the Royal Statistical Society. Series D (The Statistician), 37 (1) (1988), 2532.

    • Search Google Scholar
    • Export Citation
  • [26]

    Nadarajah, S. and Kotz, S., The beta Gumbel distribution, Mathematical Problems in Engineering, 2004 (4) (2004), 323332.

  • [27]

    Nadarajah, S. and Kotz, S., The beta exponential distribution, Reliability Engineering & System Safety, 91 (6) (2006), 689697.

  • [28]

    Ohishi, K., Okamura, H. and Dohi, T., Gompertz software reliability model: estimation algorithm and empirical validation, Journal of Systems and software, 82 (3) (2009), 535543.

    • Search Google Scholar
    • Export Citation
  • [29]

    Roozegar, R., Tahmasebi, S. and Jafari, A. A., The MCDonald Gompertz distribution: properties and applications, Communication in Statistics: Simulation and Computation, 46 (5) (2017), 33413355.

    • Search Google Scholar
    • Export Citation
  • [30]

    Silva, G. O., Ortega, E. M. and Cordeiro, G. M., The beta modified Weibull distribution, Lifetime Data Analysis, 16 (3) (2010), 409430.

    • Search Google Scholar
    • Export Citation
  • [31]

    Silva, R. C., Sanchez, J. J. D., Lima, F́. P. and Cordeiro, G. M., The Kumaraswamy Gompertz distribution, Journal ofData Science, 13 (2015), 241260.

    • Search Google Scholar
    • Export Citation
  • [32]

    Willemse, W. and Koppelaar, H., Knowledge elicitation of gompertz'law of mortality, Scandinavian Actuarial Journal, 2000 (2) (2000), 168179.

    • Search Google Scholar
    • Export Citation

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

Managing Editor

Gábor SÁGI (Rényi Institute of Mathematics)

Editorial Board

  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
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2020  
Total Cites 536
WoS
Journal
Impact Factor
0,855
Rank by Mathematics 189/330 (Q3)
Impact Factor  
Impact Factor 0,826
without
Journal Self Cites
5 Year 1,703
Impact Factor
Journal  0,68
Citation Indicator  
Rank by Journal  Mathematics 230/470 (Q2)
Citation Indicator   
Citable 32
Items
Total 32
Articles
Total 0
Reviews
Scimago 24
H-index
Scimago 0,307
Journal Rank
Scimago Mathematics (miscellaneous) Q3
Quartile Score  
Scopus 139/130=1,1
Scite Score  
Scopus General Mathematics 204/378 (Q3)
Scite Score Rank  
Scopus 1,069
SNIP  
Days from  85
sumbission  
to acceptance  
Days from  123
acceptance  
to publication  
Acceptance 16%
Rate

2019  
Total Cites
WoS
463
Impact Factor 0,468
Impact Factor
without
Journal Self Cites
0,468
5 Year
Impact Factor
0,413
Immediacy
Index
0,135
Citable
Items
37
Total
Articles
37
Total
Reviews
0
Cited
Half-Life
21,4
Citing
Half-Life
15,5
Eigenfactor
Score
0,00039
Article Influence
Score
0,196
% Articles
in
Citable Items
100,00
Normalized
Eigenfactor
0,04841
Average
IF
Percentile
13,117
Scimago
H-index
23
Scimago
Journal Rank
0,234
Scopus
Scite Score
76/104=0,7
Scopus
Scite Score Rank
General Mathematics 247/368 (Q3)
Scopus
SNIP
0,671
Acceptance
Rate
14%

 

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Studia Scientiarum Mathematicarum Hungarica
Language English
French
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Size B5
Year of
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1966
Publication
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2021 Volume 58
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ISSN 0081-6906 (Print)
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