On some properties of the mean inactivity time function

Khan, Ruhul Ali; Bhattacharyya, Dhrubasish; Mitra, Manimala

doi:10.1016/j.spl.2020.108993

Cited by 14 publications

(9 citation statements)

References 25 publications

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“…A proportional causespecific reversed hazards model was introduced by Sankaran and Anjana (2016) and Fallah et al (2021) proposed statistical inference for component lifetime distribution from coherent system lifetimes under a PRHR model. Baratnia and Doostparast (2021) proposed a new statistical method for one-way classification which is based on the RHR function of the response variable and Khan et al (2021) Kalbfleisch and Lawless (1991) or Andersen et al (2012).…”

Section: Proposed Modelmentioning

confidence: 99%

Resilience family of receiver operating characteristic curves

Khan¹

2022

Preprint

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A new semiparametric model of the ROC curve based on the resilience family or proportional reversed hazard family is proposed which is an alternative to the existing models. The resulting ROC curve and its summary indices (such as area under the curve (AUC) and Youden index) have simple analytic forms. The partial likelihood method is applied to estimate the ROC curve. Moreover, the estimation methodologies of the resilience family of the ROC curve have been developed based on AUC estimators exploiting Mann-Whitney statistics and the Rojo approach. A simulation study has been carried out to assess the performance of all considered estimators. Real data from the American National Health and Nutrition Examination Survey (NHANES) has been analysed in detail based on the proposed model and the usual binormal model prevalent in the literature. Real data in the context of brain injury-related biomarkers is also analysed in order to compare our model with the Lehmann family of the ROC curves. Finally, we show that the proposed model may be applicable in the misspecification scenario through a Ducheme muscular dystrophy data.

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Section: Proposed Modelmentioning

confidence: 99%

Resilience family of receiver operating characteristic curves

Khan¹

2022

Preprint

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“…For an unspecified m X associated with a general distribution, the formula (12) may not provide a closed form for the c.d.f. of the r.v.…”

Section: Proportional Mean Departure Time Modelmentioning

confidence: 99%

“…function is given by m(t|θ) � θm 0 (t), for all t > 0, according to the PMDT model. In spirit of (12), the c.d.f. of Y with m.d.t.…”

Section: The Model With Random Departure Indexmentioning

confidence: 99%

“…ey have many applications in various disciplines such as reliability theory, survival analysis, risk theory, and actuarial studies, among others (cf. Ortega [4], Izadkhah and Kayid [5], Jayasinghe and Zeephongsekul [6], Kayid and Izadkhah [7], Kayid et al [8], Kayid and Izadkhah [9], Bhattacharyya et al [10], Balmert et al [11], Khan et al [12], and Kayid and Alrasheedi [13]). e inactivity time at random times is one of the important notions in reliability and queuing theory (see, e.g., Kayid et al [14] and Kundu and Patra [15]).…”

Section: Introductionmentioning

confidence: 99%

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Reliability Analysis of the Proportional Mean Departure Time Model

Shrahili

Kayid

2022

Journal of Mathematics

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In this article, the mean lifetime of an individual whose lives lost based on a function of the time before which the individual has passed away is considered. The measure is used to construct a semi-parametric model called proportional mean departure time model. Examples are given and evidences are gathered to show that the model is a proper alternative for the proportional mean past lifetime model. Closure properties of the model concerning several stochastic orders and a number of reliability properties are established. Finally, the model is extended to entertain random amounts of the parameter and establish a proportional mean departure time frailty model. Further stochastic properties using several stochastic orders are developed in the context of the frailty model.

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“…Fallah et al (2021) proposed statistical inference for component lifetime distribution from coherent system lifetimes under a PRHR model. Baratnia and Doostparast (2021) proposed a new statistical method for one-way classification which is based on the RHR function of the response variable and Khan et al (2021) studied the relationship between RHR and mean inactive time function. Moreover, there exists many well known distributions which belong to the resilience parameter family.…”

Section: Introductionmentioning

confidence: 99%

Two-sample nonparametric test for proportional reversed hazards

Khan¹

2022

Preprint

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Several works have been undertaken in the context of proportional reversed hazard rate (PRHR) since last few decades. But any specific statistical methodology for the PRHR hypothesis is absent in the literature. In this paper, a two-sample nonparametric test based on two independent samples is proposed for verifying the PRHR assumption. Based on a consistent U-statistic three statistical methodologies have been developed exploiting U-statistics theory, jackknife empirical likelihood and adjusted jackknife empirical likelihood method. A simulation study has been performed to assess the merit of the proposed test procedures. Finally, the test is applied to a data in the context of brain injury-related biomarkers and a data related to Ducheme muscular dystrophy.

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On some properties of the mean inactivity time function

Cited by 14 publications

References 25 publications

Resilience family of receiver operating characteristic curves

Resilience family of receiver operating characteristic curves

Reliability Analysis of the Proportional Mean Departure Time Model

Two-sample nonparametric test for proportional reversed hazards

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