A New Compounded Model Based on Fre’chet Distribution With Application in Failure Data
الموضوعات : فصلنامه ریاضی
ّFereshteh Momeni
1
,
Kazem Fayyaz Heydari
2
,
Soheil Shokri
3
1 - دانشگاه آزاد اسلامی واحد بهشهر
2 - دانشگاه پیام نور
3 - Department of Statistics, Rasht Branch, Islamic Azad University, Rasht, Iran
الکلمات المفتاحية: Extended Frechet distribution, Power series distribution, Maximum likelihood estimation, Moments, life-time distribution,
ملخص المقالة :
Recently the Extended Fre’chet distribution (EF) has appeard as the subject of so many research. In this research, we aim to extend EF as a three-parameter distribution to a four-parameter life-time distribution named Extended Frechet Power Series (EFPS) distribution. The EFPS distribution happens to have decreasing, increasing, bathtub, and upside down bathtub hazard shapes for different values of its parameters. The maximum likelihood estimation and capability of the quantile measures are discussed. Using two data sets leading to the numerical experiment, the functioning of the maximum likelihood estimators and their asymptotic results of EFPS distribution are compared to several rival destributions.
[1] Adamidis K. and Loukas, S. (1998). A lifetime distribution with decreasing failure rate. Statistics and Probability Letters, 39, 35- 42.
[2] Alizadeh, M., Bagheri, S.F., Bahrami Samani, E., Ghobadi, S., & Nadarajah, S. (2018)
Exponentiated power Lindley power series class of distributions: Theory and applications, Communications in Statistics - Simulation and Computation, 47:9, 2499-2531.
[3] Bader, M. and Priest, A. (1982) Statistical Aspects of Fiber and Bundle Strength in Hybrid Composites. In: Hayashi, T., Kawata, S. and Umekawa, S., Eds., Progress in Science and Engineering Composites, ICCM-IV, Tokyo, 1129-1136.
[4] Bagheri, S.F, Samani, B and Ganjali. M (2015). The generalized modified Weibull power series distribution: Theory and applications. Computational Statistics and Data Analysis 00, 1–28.
[5] Barreto-Souza, W., Morais, A. L., Cordeiro, G.M. (2010). The Weibull-geometric distribution. Journal of Statistical Computation and Simulation, 81, 645- 657.
[6] Bonferroni, C.E. 1930. Elementi di statistica generale. Seeber, Firenze.
[7] Bourguignon. M Silva . R and Cordeiro G.M (2014) . A new class of fatigue life distributions. Journal of Statistical Computation and Simulation. 84(12), 2619–2635.
[8] Chahkandi, M., Ganjali, M. (2009). On some lifetime distributions with decreasing failure rate. Computational Statistics and Data Analysis, 53, 4433- 4440.
[9] Cooner, F., Banerjee, S., Carlin, B. P. and Sinha, D. (2007). Flexible cure rate modeling under latent activation schemes. Journal of the American Statistical Association, 102(478), 560–572.
[10] Eisa Mahmoudi and Mitra Shiran (2012). Exponentiated Weibull Power Series Distributions and its Applications. arXiv:1212.5613v1 [stat.ME].
[11] Gupta, P.L and Gupta, R. C (1983). On the moments of residual life in reliability and some characterization results, Communications in Statistics-Theory and Methods, 12 , 449-461.
[12] Gupta, R.C. (1981). On the mean residual life function in survival studies”, Statistical Distributions in Scientific Work, 5, 327-334.
[13] Johnson, N. L, Kemp,A. W and S. Kotz. S (2005) Univariate Discrete Distributions. John Wiley & Sons, New Jersey, 3rd edition.
[14] Kundu and Nanda ( 2010) Some Reliability Properties of the Inactivity Time. Communications in Statistics Theory and Methods. 39, 899– 911.
[15] Kus, C. A (2007). A new lifetime distribution. Computational Statistics and Data
Analysis, 51, 4497– 4509.
[16] Lu, W., Shi, D. (2011). A new compounding life distribution: theWeibull-Poisson distribution. Journal of Applied Statistics, DOI :10.1080/02664763.2011. 575126.
[17] Mahmoudi, E., Jafari, A.A. (2012). Generalized exponential power series distributions. Computational Statistics and Data Analysis, 56, 4047- 4066.
[18] Mi, J. (1996). Minimizing Some Cost Functions Related to both burn-in and field use”, Operations Research, 49, 497-500.
[19] Morais, A.L., Barreto-Souza, W. (2011). A Compound family of Weibull and Power Series Distributions. Computational Statistics and Data Analysis, 55, 1410- 1425.
[20] Min Wang (2013). A new three-parameter lifetime distribution and associated inference. arXiv:1308.4128v1 [stat.ME].
[21] Nadarajah, S. and Kotz, S. (2003). The exponentiated Fréchet distribution . InterStat. Available online from interstat. statjournals. net / YEAR/2003 / articles / 0312001.
pdf.
[22] Nanda, A. K., Singh, H., Misra, N., Paul, P. (2003). Reliability properties of reversed residual lifetime. Commun. Statist. Theor. Meth. 32(10):2031–2042.
[23] Noack, A. (1950) A class of random variables with discrete distributions, Annals of Mathematical Statistics, 21, 127-132.
26[24] Peck, D.S. and Zierdt, C.H. (1974), ”The Reliability of Semiconductor Devices in the Bell System”, Proceeding of the IEEE, 62, 185-211.
[25] Rodrigues . C , Cordeiro, G.M , Demetrio.C and Ortega. M. M (2011). The Weibull Negative Binomial Distribution. Advances and Applications in Statistics. 22(1), 25-55.
[26] Wanbo Lu and Daimin Shi (2012). A new compounding life distribution: the Weibull– Poisson distribution. Journal of Applied Statistics, 39(1), 21-38.
[27] Shafiei . S , Darijani. S and Saboori . H (2015). InverseWeibull power series distributions: properties and applications. Journal of Statistical Computation and Simulation, 1-26.
[28] Silva, R.B., Bourguignon, M., Dias, C.R.B., Cordeiro, G.M. (2013). The compound family of extended Weibull power series distributions. Computational Statistics and Data Analysis, 58, 352- 367.
[29] Smith, R.L. and Naylor, J.C. (1987). A comparison of maximum likelihood and Bayesian estimators for the three-parameterWeibull distribution, Appl. Stat. 36 , pp. 358–369.
[30] Tahmasbi, R., Rezaei, S. (2008). A two-parameter lifetime distribution with decreasing failure rate. Computational Statistics and Data Analysis, 52, 3889- 3901.
