Shapes of Hazard Functions and Lifetime Distributions

We proposed a new family of lifetime distributions, namely, complementary exponentiated exponential geometric distribution. This new family arises on a latent competing risk scenario, where the lifetime associated with a particular risk is not observable but only the maximum lifetime value among all risks. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its survival and hazard functions, moments,rth moment of theith order statistic, mean residual lifetime, and modal value. Inference is implemented via a straightforwardly maximum likelihood procedure. The practical importance of the new distribution was demonstrated in three applications where our distribution outperforms several former lifetime distributions, such as the exponential, the exponential-geometric, the Weibull, the modified Weibull, and the generalized exponential-Poisson distribution.

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Asymptotic properties of MLE’s of parameters of exponentiated exponential lifetime distributions

Communication in Statistics- Theory and Methods ◽

10.1080/03610926.2021.1882495 ◽

2021 ◽

pp. 1-15

Author(s):

James U. Gleaton ◽

Ping Sa ◽

Sami Hamid

Keyword(s):

Asymptotic Properties ◽

Lifetime Distributions

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Semiparametric likelihood inference for heterogeneous survival data under double truncation based on a Poisson birth process

Japanese Journal of Statistics and Data Science ◽

10.1007/s42081-021-00128-w ◽

2021 ◽

Author(s):

Achim Dörre

Keyword(s):

Survival Data ◽

Process Model ◽

Optimization Method ◽

Finite Sample ◽

Birth Process ◽

Dimensional Parameter ◽

Lifetime Distributions ◽

Computational Performance ◽

Semiparametric Likelihood ◽

Double Truncation

AbstractWe study a selective sampling scheme in which survival data are observed during a data collection period if and only if a specific failure event is experienced. Individual units belong to one of a finite number of subpopulations, which may exhibit different survival behaviour, and thus cause heterogeneity. Based on a Poisson process model for individual emergence of population units, we derive a semiparametric likelihood model, in which the birth distribution is modeled nonparametrically and the lifetime distributions parametrically, and define maximum likelihood estimators. We propose a Newton–Raphson-type optimization method to address numerical challenges caused by the high-dimensional parameter space. The finite-sample properties and computational performance of the proposed algorithms are assessed in a simulation study. Personal insolvencies are studied as a special case of double truncation and we fit the semiparametric model to a medium-sized dataset to estimate the mean age at insolvency and the birth distribution of the underlying population.

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Competing risks joint models using R-INLA

Statistical Modelling ◽

10.1177/1471082x20913654 ◽

2021 ◽

Vol 21 (1-2) ◽

pp. 56-71

Author(s):

Janet van Niekerk ◽

Haakon Bakka ◽

Håvard Rue

Keyword(s):

Competing Risks ◽

Count Data ◽

Joint Model ◽

Point Of View ◽

Spatial Structures ◽

Joint Models ◽

Hazard Functions ◽

Longitudinal Count Data ◽

Non Gaussian ◽

Made In

The methodological advancements made in the field of joint models are numerous. None the less, the case of competing risks joint models has largely been neglected, especially from a practitioner's point of view. In the relevant works on competing risks joint models, the assumptions of a Gaussian linear longitudinal series and proportional cause-specific hazard functions, amongst others, have remained unchallenged. In this article, we provide a framework based on R-INLA to apply competing risks joint models in a unifying way such that non-Gaussian longitudinal data, spatial structures, times-dependent splines and various latent association structures, to mention a few, are all embraced in our approach. Our motivation stems from the SANAD trial which exhibits non-linear longitudinal trajectories and competing risks for failure of treatment. We also present a discrete competing risks joint model for longitudinal count data as well as a spatial competing risks joint model as specific examples.

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The Imprecise Logit-Normal Model and its Application to Estimating Hazard Functions

Journal of Statistical Theory and Practice ◽

10.1080/15598608.2009.10411919 ◽

2009 ◽

Vol 3 (1) ◽

pp. 183-195 ◽

Cited By ~ 4

Author(s):

Miķelis Bickis

Keyword(s):

Normal Model ◽

Hazard Functions

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Insensitivity of steady-state distributions of generalized semi-Markov processes by speeds

Advances in Applied Probability ◽

10.1017/s0001867800031402 ◽

1978 ◽

Vol 10 (04) ◽

pp. 836-851 ◽

Cited By ~ 2

Author(s):

R. Schassberger

Keyword(s):

Steady State ◽

General System ◽

State Distribution ◽

Lifetime Distributions ◽

State Dependent ◽

Semi Markov Process ◽

Semi Markov Processes ◽

Infinite State ◽

State Case ◽

Residual Lifetimes

A generalized semi-Markov process with speeds describes the fluctuation, in time, of the state of a certain general system involving, at any given time, one or more living components, whose residual lifetimes are being reduced at state-dependent speeds. Conditions are given for the stationary state distribution, when it exists, to depend only on the means of some of the lifetime distributions, not their exact shapes. This generalizes results of König and Jansen, particularly to the infinite-state case.

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