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An extension of exponentiated Lomax distribution with application to lifetime data. (English) Zbl 1486.62040


MSC:

62E15 Exact distribution theory in statistics
60E05 Probability distributions: general theory
60E15 Inequalities; stochastic orderings
62N05 Reliability and life testing

References:

[1] Plots of the estimated pdf and cdf of the APTEL distribution together with other competitor distributions for the second data set are demonstrated in Figure 5. Also, P-P plots of the APTEL and other fitted distributions are displayed in Figure 6. Tables 3 and 4 indicate that APTEL distribution gives the best fit and thus demonstrates superiority over the examined lifetime distributions in modeling the lifetime data sets under study. This conclusion was further supported by inspecting the PP plots, the density and cumulative distribution fit of the distributions for the real lifetime data sets. The total time test (TTT) used for verifying the validity of the model. It allows identifying the shape of hrf graphically. Aarset (1987) showed that the hrf is constant if the TTT plot is graphically presented as a straight diagonal, the hrf is increasing (or decreasing) if the TTT plot is concave (or convex). The hrf is U-shaped (bathtub) if the TTT plot is firstly convex and then concave, if not, the hrf is unimodal. Figure 7 shows that the TTT plot is a unimodal; therefore it verifies our model validity. References Abdul-Moniem IB, Abdel-Hameed HF. On exponentiated Lomax distribution. Int J Math Arch. 2012; 33(5): 1-7.
[2] Ashour SK, Eltehiwy MA. Transmuted exponentiated Lomax distribution. Aust J Basic Appl Sci. 2013; 7(7): 658-667.
[3] Afify AZ, Nofal ZM, Yousof HM, El Gebaly YM, Butt NS. The transmuted Weibull Lomax distribution: properties and application. Pak J Stat Oper Res. 2015; 11(1): 135-152. · Zbl 1509.60022
[4] Al-Zahrani B. An extended Poisson-Lomax distribution. Adv Math Sci J. 2015; 4(2): 79-89. · Zbl 1336.60017
[5] Aarset MV. How to identify a bathtub hazard rate. IEEE Trans Reliab. 1987; 36(1): 106-108. · Zbl 0625.62092
[6] Balkema AA, de Hann L. Residual life at great age, Ann Prob. 1974; 2: 972-804.
[7] Chahkandi M, Ganjali M. On some lifetime distributions with decreasing failure rate. Comput Stat Data Anal. 2009; 53(13): 4433-4440. · Zbl 1298.62175
[8] Cordeiro GM, Ortega E, Popović B. The gamma-Lomax distribution. J Stat Comput Simul. 2015; 85(2): 305-319. · Zbl 1457.62308
[9] Cordeiro GM, Ortega EMM, Cunha DCC. The exponentiated generalized class of distributions. J Data Sci. 2013; 11: 1-27.
[10] Dey S, Alzaatreh A, Zhang C, Kumar D. A new extension of generalized exponential distribution with application to Ozone data. Ozone Sci Eng. 2017; 39 (4): 273-285.
[11] Dey S, Nassr M, Kumar D. Alpha power transformed inverse Lindley distribution: A distribution with upside-down bathtub-shaped hazard function. J Comput Appl Math. 2018; 348(1): 130-145. · Zbl 1404.60028
[12] Elbatal I, Kareem A. Statistical properties of Kumaraswamy exponentiated Lomax distribution. J Mod Math Stat. 2014; 8(1): 1-7.
[13] El-Bassiouny AH, Abdo NF, Shahen HS. Exponential Lomax distribution. Int J Comput Appl. 2015; 121(13): 24-29.
[14] Ghitany ME, AL-Awadhi FA, Alkhalfan LA. Marshall-Olkin extended Lomax distribution and its applications to censored data. Commun Stat Theory Methods. 2007; 36 (10): 1855-1866. · Zbl 1122.62081
[15] Gupta RC, Gupta RD, Gupta PL. Modeling failure time data by Lehman alternatives. Commun Stat Theory Methods. 1998; 27(4): 887-904. · Zbl 0900.62534
[16] Hassan AS, Abd-Alla M. Exponentiated Lomax geometric distribution: properties and applications. Pak J Stat Oper Res. 2017; 13(3): 545-566. · Zbl 1509.60040
[17] Hassan AS, Abd-Allah M. Exponentiated Weibull-Lomax distribution: properties and estimation. J Data Sci. 2018; 16(2): 277-298.
[18] Hassan AS, Abd-Allah M. On inverse power Lomax distribution. J Data Sci. 2019; 6(2): 259-278.
[19] Hassan AS, Al-Ghamdi A. Optimum step stress accelerated life testing for Lomax distribution. J Appl Sci Res. 2009; 5(12): 2153-2164.
[20] Hassan AS, Mohamed RE. Parameter estimation of inverse exponentiated Lomax with right censored data. Gazi Univer J Sci. 2019; 32(4): 1370-1386.
[21] Hassan AS, Nassr SG. Power Lomax Poisson distribution: properties and estimation. J Data Sci. 2018; 18(1): 105-128.
[22] Thailand Statistician, 2021; 19(3): 484-500 · Zbl 1486.62040
[23] Hassan AS, Assar MS, Shelbaia A. Optimum step-stress accelerated life test plan for Lomax distribution with an adaptive type-II progressive hybrid censoring. Br J Math Comput Sci. 2016; 13(2): 1-19.
[24] Hassan AS, Mohamed RE, Elgarhy M, Alrajhi S. On the alpha power transformed power Lindley distribution. J Prob Stat. 2019; 1-13. · Zbl 1431.62055
[25] Hassan AS, Mohamed RE, Elgarhy M, Fayomic A. Alpha power transformed extended exponential distribution: properties and applications. J Nonlinear Sci Appl. 2018; 12: 239-251.
[26] Johnson NL, Kotz S, Balakrishnan N. Continuous Univariate Distribution. New York: John Wiley & Sons. 1995. · Zbl 0821.62001
[27] Lee ET. Statistical Methods for Survival Data Analysis. New York: John Wiley & Sons.1992.
[28] Lemonte AJ, Cordeiro GM. An extended Lomax distribution. Statistics. 2013; 47(4): 800-816. · Zbl 1440.62062
[29] Lomax KS. Business failures: another example of the analysis of failure data. J Am Stat Assoc. 1954; 49: 847-852. · Zbl 0056.13702
[30] Mahdavi A, Kundu D. A new method of generating distribution with an application to exponential distribution. Commun Stat Theory Methods. 2017; 46(13): 6543-6557. · Zbl 1391.62022
[31] Nassr M, Alaatreh A, Mead M, Abo-Kasem OE. Alpha power Weibull distribution: properties and applications Commun Stat Theory Methods. 2017; 46(20): 10236-10252. · Zbl 1386.60060
[32] Oguntunde PE, Khaleel MA, Ahmed MT, Adejumo AO, Odetunmibi OA. A new generalization of the Lomax distribution with increasing, decreasing, and constant failure rate. Model Simul Eng. 2017; 1-6.
[33] Owoloko EA, Oguntunde PE, Adejumo AO. Performance rating of the transmuted exponential distribution: an analytical approach. SpringerPlus. 2015; 4: 818.
[34] Rady EA, Hassanein, WA, Elhaddad TA. The power Lomax distribution with an application to bladder cancer data. SpringerPlus. 2016; 5: 1838.
[35] Tahir MH, Cordeiro GM, Mansoor M, and Zubair M. The Weibull-Lomax distribution: properties and applications. Hacet J Math Stat. 2015; 44 (2): 461-480. · Zbl 1326.60023
[36] Tahir MH, Hussain MA, Cordeiro GM, Hamedani GG, Mansoor M, Zubair M. The Gumbel-Lomax distribution: properties and applications. J Stat Theory Appl. 2016; 15 (1): 61-79.
[37] Shaked M, Shanthikumar JG. Stochastic Orders. New York: John Wiley & Sons; 2007.
[38] Swain J, Venkatraman S, Wilson J. Least squares estimation of distribution function in Johnson’s translation system. J Stat Comput Simul. 1988; 29: 271-297.
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