A new upside-down bathtub shaped hazard rate model for survival data analysis.

*(English)*Zbl 1334.62177Summary: In medical, engineering besides demography and other applied disciplines, it is pronounced in some applications that the hazard rate of the data initially increased to a pick in the beginning age, declined abruptly till it stabilized. In statistics literature, such hazard rate is known as the upside-down bathtub shaped hazard rate and propound in the various survival studies. In this paper, we proposed a transmuted inverse Rayleigh distribution, which possesses the upside-down bathtub shape for its hazard rate. The fundamental properties such as mean, variance, mean deviation, order statistics, Renyi entropy and stress-strength reliability of the proposed model are explored here. Further, three methods of estimation namely maximum likelihood, least squares and maximum product spacings methods are used for estimating the unknown parameters of the transmuted inverse Rayleigh distribution, and compared through the simulation study. Finally, the applicability of the proposed distribution is shown for a set of real data representing the times between failures of the secondary reactor pumps.

##### MSC:

62N05 | Reliability and life testing |

62E15 | Exact distribution theory in statistics |

60E05 | Probability distributions: general theory |

##### Keywords:

transmuted inverse Rayleigh model; upside-down bathtub shaped hazard rate; statistical inference; goodness-of-fit
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\textit{V. K. Sharma} et al., Appl. Math. Comput. 239, 242--253 (2014; Zbl 1334.62177)

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##### References:

[1] | Aarset, M. V., How to identify a bathtub hazard rate, IEEE Trans. Reliab., 36, (1987) · Zbl 0625.62092 |

[2] | Aryal, G. R.; Tsokos, C. P., On the transmuted extreme value distribution with application, Nonlinear Anal., 71, e1401-e1407, (2009) · Zbl 1238.60018 |

[3] | Aryal, G. R.; Tsokos, C. P., Transmuted Weibull distribution: a generalization of the Weibull probability distribution, Eur. J. Pure Appl. Math., 4, 89-102, (2011) · Zbl 1389.62150 |

[4] | Bennette, S., Log-logistic regression models for survival data, Appl. Stat., 32, 165-171, (1983) |

[5] | Cheng, R.; Amin, N., Estimating parameters in continuous univariate distributions with a shifted origin, J. R. Stat. Soc. Ser. B Methodol., 45, 394-403, (1983) · Zbl 0528.62017 |

[6] | Efron, B., Logistic regression, survival analysis, and the kaplan-meier curve, J. Am. Stat. Assoc., 83, 414-425, (1988) · Zbl 0644.62100 |

[7] | Langlands, A.; Pocock, S.; Kerr, G.; Gore, S., Long-term survival of patients with breast cancer: a study of the curability of the disease, Br. Med. J., 2, 1247-1251, (1997) |

[8] | Merovci, F., Transmuted Lindley distribution, Int. J. Open Probl. Comput. Sci. Math., 6, (2013) |

[9] | Merovci, F., Transmuted Rayleigh distribution, Austrian J. Stat., 42, 21-31, (2013) |

[10] | Renyi, A., On measures of entropy and information, (Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, (1961), University of California Press Berkeley) · Zbl 0106.33001 |

[11] | H. Schbe, A spot of an upside down bathtub failure rate lifetime distribution in the wild Avialable at <http://www.nottingham.ac.uk/engineering/conference/ar2ts/documents/33.pdf>. |

[12] | Suprawhardana, M.; Prayoto; Sangadji, Total time on test plot analysis for mechanical components of the rsg-gas reactor, Atom Inones, 25, (1999) |

[13] | W.T. Shaw, I.R.C. Buckley, The alchemy of probability distributions: beyond gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map, 2009, Article ID: arXiv:0901.0434 [q-fin.ST]. Available at <http://arxiv.org/pdf/0901.0434.pdf>. |

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