Properties and applications of beta Erlang-truncated exponential distribution
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Authors
M. Shrahili
- Department of Statistics and Operations Research, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia.
I. Elbatal
- Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Saudi Arabia.
- Faculty of Graduate Studies for Statistical Research, Cairo University, Egypt.
Isyaku Muhammad
- Department of Mechanical Engineering, School of Technology, Kano State Polytechnic, Nigeria.
Mustapha Muhammad
- Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University Kano (BUK), Nigeria.
Abstract
In this article, we proposed a new four-parameter distribution called beta Erlang truncated exponential
distribution (BETE). Some important mathematical and statistical properties of the proposed distribution are examined.
The stochastic ordering result for the BETE was also discussed. Moreover, the \(r^{\rm th}\) moment, moment generating function, incomplete moments, mean deviations, Bonferroni and Lorenz curves, moments of residual life, Shannon and Renyi entropies, and Kullback--Leibler divergence measure are derived. The maximum-likelihood estimate for the unknown parameters of the BETE was established and assessed by the simulation studies. The maximum likelihood estimation of the stress-strength parameter is discussed and its asymptotic distribution is obtained.
The effectiveness and usefulness of the BETE are demonstrated by the use of three real data set, in which the BETE provide a better fit than some other existing distributions and demonstrated its capability in the stress-strength reliability analysis.
Share and Cite
ISRP Style
M. Shrahili, I. Elbatal, Isyaku Muhammad, Mustapha Muhammad, Properties and applications of beta Erlang-truncated exponential distribution, Journal of Mathematics and Computer Science, 22 (2021), no. 1, 16--37
AMA Style
Shrahili M., Elbatal I., Muhammad Isyaku, Muhammad Mustapha, Properties and applications of beta Erlang-truncated exponential distribution. J Math Comput SCI-JM. (2021); 22(1):16--37
Chicago/Turabian Style
Shrahili, M., Elbatal, I., Muhammad, Isyaku, Muhammad, Mustapha. "Properties and applications of beta Erlang-truncated exponential distribution." Journal of Mathematics and Computer Science, 22, no. 1 (2021): 16--37
Keywords
- Erlang-truncated exponential distribution
- beta-G distribution
- moments
- entropy
- maximum likelihood estimation
- stress-strength parameter estimation
MSC
References
-
[1]
T. H. M. Abouelmagda, M. S. Hameda, L. Handiqueb, H. Goualc, M. M. Alid, H. M. Yousofe, N. C. Korkmazf, A new class of distributions based on the zero truncated Poisson distribution with properties and applications, J. Nonlinear Sci. Appl., 12 (2019), 152--164
-
[2]
K. A. Adepoju, A. Chukwu, M. Wang, The Beta Power Exponential Distribution, J. Stat. Sci. Appl., 2 (2014), 37--46
-
[3]
Z. Ahmad, M. Elgarhy, N. Abbas, A new extended alpha power transformed family of distributions: properties and applications, J. Statist. Model. Theory Appl., 1 (2018), 13--28
-
[4]
Z. Ahmad, M. Elgarhy, G. G. Hamedani, A new Weibull-X family of distributions: properties, characterizations and applications, J. Stat. Distrib. Appl., 5 (2018), 18 pages
-
[5]
A. Akinsete, F. Famoye, C. Lee, The beta-Pareto distribution, Statistics, 42 (2008), 547--563
-
[6]
M. Alizadeh, M. Rasekhi, H. M. Yousof, G. G. Hamedani, The transmuted Weibull-G family of distributions, Hacet. J. Math. Stat., 47 (2018), 1671--1689
-
[7]
M. G. Bader, A. M. Priest, Statistical aspects of fiber and bundle strength in hybrid composites, Progress in Science and Engineering of Composites, 1982 (1982), 1129--1136
-
[8]
R. A. R. Bantan, F. Jamal, C. Chesneau, M. Elgarhy, Type II Power Topp-Leone Generated Family of Distributions with Statistical Inference and Applications, Symmetry, 12 (2020), 24 pages
-
[9]
R. E. Barlow, F. Proschan, Statistical theory of Reliability and life testing, Holt, Rinehart and Winston, New York-Montreal (1975)
-
[10]
W. Barreto-Souza, G. M. Cordeiro, A. B. Simas, Some results for beta Frechet distribution, Comm. Statist. Theory Methods, 40 (2011), 798--811
-
[11]
W. Barreto-Souza, A. H. S. Santos, G. M. Cordeiro, The beta generalized exponential distribution, J. Stat. Comput. Simul., 80 (2010), 159--172
-
[12]
Z. W. Birnbaum, S. C. Saunders, Estimation for a family of life distributions with applications to fatigue, J. Appl. Probability, 6 (1969), 328--347
-
[13]
P. J. Boland, T. Hu, M. Shaked, J. G. Shanthikumar, Stochastic ordering of order statistics II, in: Modeling uncertainty, 2005 (2005), 607--623
-
[14]
P. J. Boland, M. Shaked, J. G. Shanthikumar, Stochastic ordering of order statistics, Handbook of Statistics, 1988 (1998), 89--103
-
[15]
G. Casella, R. L. Berger, Statistical Inference, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove (1990)
-
[16]
G. M. Cordeiro, A. J. Lemonte, The $\beta$-Birnbaum-Saunders distribution: an improved distribution for fatigue life modeling, Comput. Statist. Data Anal., 55 (2011), 1445--1461
-
[17]
G. M. Cordeiro, A. J. Lemonte, The beta Laplace distribution, Statist. Probab. Lett., 81 (2011), 973--982
-
[18]
G. M. Cordeiro, A. J. Lemonte, The beta-half-Cauchy distribution, J. Probab. Stat., 2011 (2011), 18 pages
-
[19]
G. M. Cordeiro, A. B. Simas, B. D. Stosic, Explicit expressions for moments of the beta Weibull distribution, arXiv, 2008 (2008), 17 pages
-
[20]
A. R. El-Alosey, Random sum of new type of mixture of distribution, Int. J. Statist. Syst., 2 (2007), 49--57
-
[21]
N. Eugene, C. Lee, F. Famoye, Beta-normal distribution and its applications, Comm. Statist. Theory Methods, 31 (2002), 497--512
-
[22]
R. E. Glaser, Bathtub and related failure rate characterizations, J. Amer. Statist. Assoc., 75 (1980), 667--672
-
[23]
A. A. Jafari, S. Tahmasebi, M. Alizadeh, The beta-Gompertz distribution, Rev. Colombiana Estadist., 37 (2014), 141--158
-
[24]
E. Mahmoudi, The beta generalized Pareto distribution with application to lifetime data, Math. Comput. Simulation, 81 (2011), 2414--2430
-
[25]
M. Muhammad, Generalized Half Logistic Poisson Distributions, Comm. Stat. Appl. Methods, 24 (2017), 353--365
-
[26]
M. Muhammad, Poisson-odd generalized exponential family of distributions: theory and applications, Hacet. J. Math. Stat., 47 (2018), 1652--1670
-
[27]
M. Muhammad, L. Liu, A New Extension of the Generalized Half Logistic Distribution with Applications to Real Data, Entropy, 21 (2019), 37 pages
-
[28]
S. Nadarajah, S. Kotz, The beta Gumbel distribution, Math. Probl. Eng., 2004 (2004), 323--332
-
[29]
S. Nadarajah, S. Kotz, The beta exponential distribution, Reliab. Eng. Syst. Safety, 91 (2006), 689--697
-
[30]
A. K. Nanda, S. Das, Stochastic orders of the Marshall-Olkin extended distribution, Statist. Probab. Lett., 82 (2012), 295--302
-
[31]
V. Nekoukhou, The Beta-Rayleigh Distribution on the Lattice of Integers, J. Statist. Res. Iran, 12 (2015), 205--224
-
[32]
V. Nekoukhou, M. H. Alamatsaz, A family of skew-symmetric-Laplace distributions, Statist. Papers, 53 (2012), 685--696
-
[33]
M. D. Nichols, W. J. Padgett, A bootstrap control chart for Weibull percentiles, Quality Reliab. Eng. Int., 22 (2006), 141--151
-
[34]
I. E. Okorie, A. C. Akpanta, J. Ohakwe, Marshall--Olkin generalized Erlang--truncated exponential distribution: Properties and applications, Cogent Math., 4 (2017), 19 pages
-
[35]
I. E. Okorie, A. C. Akpanta, J. Ohakwe, D. C. Chikezie, The Extended Erlang-Truncated Exponential distribution: Properties and application to rainfall data, Heliyon, 3 (2017), 12 pages
-
[36]
P. F. Paranaíba, E. M. M. Ortega, G. M. Cordeiro, R. R. Pescim, The beta Burr XII distribution with application to lifetime data, Comput. Statist. Data Anal., 55 (2011), 1118--1136
-
[37]
R. R. Pescim, C. G. B. Demétrio, G. M. Cordeiro, E. M. Ortega, M. R. Urbano, The beta generalized half-normal distribution, Comput. Statist. Data Anal., 54 (2010), 945--957
-
[38]
S. M. Ross, Stochastic processes, Second ed., John Wiley & Sons, New York (1996)
-
[39]
A. Saboor, M. N. Khan, G. M. Cordeiro, I. Elbatal, R. R. Pescim, The Beta exponentiated Nadarajah-Haghighi distribution: Theory, regression model and application, Math. Slovaca, 69 (2019), 939--952
-
[40]
M. Shaked, J. G. Shanthikumar, J. B. Valdez-Torres, Discrete probabilistic orderings in reliability theory, Statist. Sinica, 4 (1994), 567--579
-
[41]
M. K. Shakhatreh, A. Yusuf, A. R. Mugdadi, The beta generalized linear exponential distribution, Statistics, 50 (2016), 1346--1362
-
[42]
G. O. Silva, E. M. M. Ortega, G. M. Cordeiro, The beta modified Weibull distribution, Lifetime Data Anal., 16 (2010), 409--430
-
[43]
D. Stoyan, Comparison methods for queues and other stochastic models, John Wiley & Sons, Chichester (1983)
-
[44]
K. Zografos, N. Balakrishnan, On families of beta and generalized gamma-generated distributions and associated inference, Stat. Methodol., 6 (2009), 344--362