Hazard Rate Distribution Research Articles

Some bivariate Schur-constant distributions and application to life insurance

Schur-constant models play a particular role when modelling time in fields such as actuarial science, insurance, reliability and survival models. These models describe random lifetimes with a certain dependence. In this study, a relation between proportional hazard rate distributions and Schur-constant models is established. Bivariate Schur-constant models, whose marginals are proportional hazard rate distributed, are introduced. Then, the dependency analysis in life insurances is performed through Schur-constant and copula models. It is revealed that there are differences in pricing when individuals' future lifetimes are dependent.

Robust safety monitoring and signal detection using alternatives to the standard poisson distribution

ABSTRACT Proper and timely characterization of the safety profile of a pharmaceutical product under development is imperative for assessing the overall benefit-risk relationship of the product and for making key development decisions. For ongoing clinical development, a comprehensive and robust safety monitoring and safety signal detection program which is based upon quantitative statistical reasoning is critical. Methods presented here can be applied to safety signal detection and periodic safety monitoring. Various statistical properties, distributions, and models, all utilizing a Bayesian framework are considered and further examined in order to identify robust methods applicable to a broad set of scenarios and situations. Methods developed for incidence counts (including those with under-dispersed distributions) with variable time-at-risk and with underlying constant or non-constant hazard rates, are proposed and compared to traditional methods designed to assess adverse event incidence rates or binomial incidence proportions (which assume an underlying constant hazard rate and subsequent Poisson distribution for modeling event counts).

Moments of Generalized Order Statistics from Doubly Truncated Power Linear Hazard Rate Distribution

Moments of Generalized Order Statistics from Doubly Truncated Power Linear Hazard Rate Distribution

Extended power hazard rate distribution and its application

A new model four-parameter model called the odd generalized exponential power hazard rate (OGE-PHR) distribution has been introduced. Some statistical properties for OGE-PHR are obtained. The moments, quantile, mode, reliability, and order statistics are discussed. Estimation of parameters, maximum likelihood technique is employed. Two real data sets are discussed with applications.

Statistical Inference of Power Hazard Rate Distribution in the Presence of Competing Risks Model with Application

Statistical Inference of Power Hazard Rate Distribution in the Presence of Competing Risks Model with Application

Reliability estimation for bathtub-shaped distribution under block progressive censoring

In this article, estimates of reliability performance characteristics are discussed when life test is conducted upon various test facilities under block progressive Type-II censoring. When the differences in different test facilities are taken into account and the lifetime of products follows a bathtub-shaped hazard rate distribution, different estimates are obtained from classical and hierarchical Bayesian frameworks, respectively. Existence and uniqueness of maximum likelihood estimators of model parameters are established, and approximate confidence intervals are obtained as well based on asymptotic theory and delta method. Moreover, associated Bayes estimators are also evaluated using a hybrid Metropolis–Hasting sampling in hierarchical framework. Finally, performances of the proposed approaches are compared via extensive simulation study, and a real data example is also presented for application viewpoint.

The Value of Observing the Buyers’ Arrival Time in Dynamic Pricing

We consider a dynamic pricing problem in which a firm sells one item to a single buyer to maximize expected revenue. The firm commits to a price function over an infinite horizon. The buyer arrives at some random time with a private value for the item. He is more impatient than the seller and strategizes over the timing of the purchase in order to maximize his expected utility, which implies either buying immediately, waiting to benefit from a lower price, or not buying. We study the value of the seller’s ability to observe the buyer’s arrival time in terms of her expected revenue. When the seller can observe the buyer’s arrival, she can make the price function contingent on the buyer’s arrival time. On the contrary, when the seller can’t, her price function is fixed at time zero for the whole horizon. The value of observability (VO) is defined as the worst-case ratio between the expected revenue of the seller when she observes the buyer’s arrival and that when she does not. First, we show that, for the particular case in which the buyer’s valuation follows a monotone hazard rate distribution, the upper bound of VO is [Formula: see text]. Next, we show our main result: in a setting very general on valuation and arrival time distributions: VO is at most 4.911. To obtain this bound, we fully characterize the solution to the observable arrival problem and use this solution to construct a random and periodic price function for the unobservable case. Finally, we show by solving a particular example to optimality that VO has a lower bound of 1.136. This paper was accepted by Itai Ashlagi, revenue management and market analytics. Funding: This work was partially supported by the Agencia Nacional de Investigación y Desarrollo Chile [Grants ACT210005 and FONDECYT 1220054], and by the Center for Mathematical Modeling at the University of Chile [Grant FB210005]. The work of D. Pizarro has benefited from the Artificial and Natural Intelligence Toulouse Institute, which is funded by the French “Investing for the Future – PIA3” program [Grant ANR-19-P3IA-0004]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2023.4794 .

Estimation of Dependent Competing Risks Model with Baseline Proportional Hazards Models under Minimum Ranked Set Sampling

The ranked set sampling (RSS) is an efficient and flexible sampling method. Based on a modified RSS named minimum ranked set sampling samples (MinRSSU), inference of a dependent competing risks model is proposed in this paper. Then, Marshall–Olkin bivariate distribution model is used to describe the dependence of competing risks. When the competing risks data follow the proportional hazard rate distribution, a dependent competing risks model based on MinRSSU sampling is constructed. In addition, the model parameters and reliability indices were estimated by the classical and Bayesian method. Maximum likelihood estimators and corresponding asymptotic confidence intervals are constructed by using asymptotic theory. In addition, the Bayesian estimator and highest posterior density credible intervals are established under the general prior. Furthermore, according to E-Bayesian theory, the point and interval estimators of model parameters and reliability indices are obtained by a sampling algorithm. Finally, extensive simulation studies and a real-life example are presented for illustrations.

A Bivariate Extension to Exponentiated Inverse Flexible Weibull Distribution: Shock Model, Features, and Inference to Model Asymmetric Data

The primary objective of this article was to introduce a new probabilistic model for the discussion and analysis of random covariates. The introduced model was derived based on the Marshall–Olkin shock model. After proposing the mathematical form of the new bivariate model, some of its distributional properties, including joint probability distribution, joint reliability distribution, joint reversed (hazard) rate distribution, marginal probability density function, conditional probability density function, moments, and distributions for both Y=max{X1,X2} and W=min{X1,X2}, were investigated. This novel model can be applied to discuss and evaluate symmetric and asymmetric data under various kinds of dispersion. Moreover, it can be used as a probability approach to analyze different shapes of hazard rates. The maximum likelihood approach was utilized for estimating the parameters of the bivariate model. A simulation study was carried out to assess the performance of the parameters, and it was noted that the maximum likelihood technique can be used to generate consistent estimators. Finally, two real datasets were analyzed to illustrate the notability of the novel bivariate distribution, and it was found that the suggested distribution provided a better fit than the competitive bivariate models.

Doubly Truncated Power- Hazard Rate Distribution via Generalized Order Statistics

The paper highlights the moments characteristics of the doubly truncated power hazard rate distribution via generalized order statistics. The particular cases and several deductions are explained. The characterization result has also deliberated. Additionally, some numerical computations through R software are listed.

The length-biased power hazard rate distribution: Some properties and applications

Abstract In this article, the length-biased power hazard rate distribution has introduced and investigated several statistical properties. This distribution reports an extension of several probability distributions, namely: exponential, Rayleigh, Weibull, and linear hazard rate. The procedure of maximum likelihood estimation is taken for parameters. Finally, the applicability of the model is explored by three real data sets. To examine, the performance of the technique, a simulation study is extracted.

데이터 기반 지상용 변압기의 잔여수명과 고장확률(PoF) 도출방안 연구

In Korea, as power facilities are aging like overseas nations, maintenance and replacement costs of power facilities are expected to increase rapidly. In order to operate power facilities with a limited budget efficiently, it is necessary to introduce Asset Management System (AMS) in maintenance of the power facility in line with the global trend. To this end, it is essential for power companies to predict the remaining lifetime of power facilities and develop Probability of Failure (PoF) in their own way depending on the type and operating conditions of power facilities. Existing studies only calculated the statistical life expectancy of the power facility, but in this study, both of the statistical life expectancy and the condition remaining lifetime are presented in order to assess the PoF of power facility, in which the statistical life expectancy is calculated by using Weibull distributions. In this study, we present the criteria for determining the condition remaining lifetime using Health Index, inspection and diagnosis data of the pad mounted transformer operated by Korea Electric Power Corporation (KEPCO) in the field. In addition, the final remaining lifetime of the pad mounted transformer was derived through the folding function and was converted into PoF using Hazard rate distribution based on the apparent age. PoF derived in this study is expected to be used in the risk matrix of the AMS and useful in establishing the systematic maintenance plan of the pad mounted transformer.

Overt Oculomotor Behavior Reveals Covert Temporal Predictions.

Our eyes move in response to stimulus statistics, reacting to surprising events, and adapting to predictable ones. Cortical and subcortical pathways contribute to generating context-specific eye-movement dynamics, and oculomotor dysfunction is recognized as one the early clinical markers of Parkinson's disease (PD). We asked if covert computations of environmental statistics generating temporal expectations for a potential target are registered by eye movements, and if so, assuming that temporal expectations rely on motor system efficiency, whether they are impaired in PD. We used a repeating tone sequence, which generates a hazard rate distribution of target probability, and analyzed the distribution of blinks when participants were waiting for the target, but the target did not appear. Results show that, although PD participants tend to produce fewer and less temporally organized blink events relative to healthy controls, in both groups blinks became more suppressed with increasing target probability, leading to a hazard rate of oculomotor inhibition effects. The covert generation of temporal predictions may reflect a key feature of cognitive resilience in Parkinson's Disease.

Pricing with Samples

This paper studies the value of data for pricing purposes. Although pricing is central across industries, little is known about the minimal amount of data needed to achieve good pricing decisions. The present paper proposes a novel approach to quantify the informational content of data, through the introduction of a new class of robust data-driven policies and the development of factor-revealing dynamic programs. Studying the prototypical case of data coming in the form of samples from the willingness to pay of customers, we show that even a few samples (as few as 10) go a very long way in uncovering “good” prices. For example, quite strikingly, against a general class of distributions (monotone increasing hazard rate distributions), a single observation guarantees 64% of the performance an oracle with full knowledge of the distribution would achieve, two samples suffice to ensure 71%, and 10 samples guarantee 80% of such performance.

Discrete distributions with bathtub-shaped hazard rates

Discrete distributions with bathtub shaped hazard rates have recently become of interest in reliability modelling and analysis. In the present work, we address the problem of obtaining distributions having such hazard rates when the lifetime is discrete. The methods considered here include discretising continuous bathtub models, construction using the score function, construction from decreasing hazard rate distributions and some other methods currently available in the continuous case. We discuss properties and applications of the discretised quadratic hazard model which has a bathtub shaped hazard rate. Keywords: Bathtub hazard rate, Discrete distribution, Quadratic hazard model, Score function, Upside down bathtub hazard rate

Third-degree price discrimination versus uniform pricing

We compare the profit of the optimal third-degree price discrimination policy against a uniform pricing policy. A uniform pricing policy offers the same price to all segments of the market. Our main result establishes that for a broad class of third-degree price discrimination problems with concave profit functions (in the price space) and common support, a uniform price is guaranteed to achieve one half of the optimal monopoly profits. This profit bound holds for any number of segments and prices that the seller might use under third-degree price discrimination. We establish that these conditions are tight and that weakening either common support or concavity can lead to arbitrarily poor profit comparisons even for regular or monotone hazard rate distributions.

A Flexible Bathtub-Shaped Failure Time Model: Properties and Associated Inference

In this study, we introduce an extended version of the modified Weibull distribution with an additional shape parameter, in order to provide more flexibility to its density and the hazard rate function. The distribution is capable of modeling the bathtub-shaped, decreasing, increasing and the constant hazard rate function. The proposed model contains sub-models that are widely used in lifetime data analysis such as the modified Weibull, Chen, extreme value, Weibull, Rayleigh, and exponential distributions. We study its statistical properties which include the hazard rate function, moments and distribution of the order statistics. The parameters involved in the model are estimated by using maximum likelihood and the Bayesian method of estimation. In Bayesian estimation, we assume independent Gamma priors for the parameters and MCMC technique such as the Metropolis-Hastings algorithm within Gibbs sampler has been implemented to obtain the sample-based estimators and the highest posterior density intervals of the parameters. Tierney and Kadane (1986) approximation is also used to obtain Bayes estimators of the parameters. In order to highlight the relative importance of various estimates obtained, a simulation study is carried out. The usefulness of the proposed model is illustrated using two real datasets.

Inference for the power-exponential hazard rate distribution under progressive type-II censored data

In this paper, we consider the problem of estimation and prediction from a new lifetime distribution called the power-exponential hazard rate distribution under progressively type-II right censored sample. The maximum likelihood (ML) estimates and the Bayes estimates of the unknown parameters under some symmetric and asymmetric loss functions via the Metropolis-Hastings algorithm are derived. The asymptotic confidence interval, some bootstrap confidence intervals and the HPD credible interval for the parameters are proposed as well. In regard to prediction problem, the ML and Bayesian methods are used to predict the future censored observations. A real data is provided to illustrate the proposed methods of estimation and prediction. Finally, the performance of proposed point estimators and confidence intervals are evaluated in a simulation study.

Generalized proportional reversed hazard rate distributions with application in medicine

Generalized proportional reversed hazard rate distributions with application in medicine

Optimal Pricing for MHR and λ-regular Distributions

We study the performance of anonymous posted-price selling mechanisms for a standard Bayesian auction setting, where n bidders have i.i.d. valuations for a single item. We show that for the natural class of Monotone Hazard Rate (MHR) distributions, offering the same, take-it-or-leave-it price to all bidders can achieve an (asymptotically) optimal revenue. In particular, the approximation ratio is shown to be 1+ O (ln ln n / ln n ), matched by a tight lower bound for the case of exponential distributions. This improves upon the previously best-known upper bound of e /( e −1)≈ 1.58 for the slightly more general class of regular distributions. In the worst case (over n ), we still show a global upper bound of 1.35. We give a simple, closed-form description of our prices, which, interestingly enough, relies only on minimal knowledge of the prior distribution, namely, just the expectation of its second-highest order statistic. Furthermore, we extend our techniques to handle the more general class of λ-regular distributions that interpolate between MHR (λ =0) and regular (λ =1). Our anonymous pricing rule now results in an asymptotic approximation ratio that ranges smoothly, with respect to λ, from 1 (MHR distributions) to e /( e −1) (regular distributions). Finally, we explicitly give a class of continuous distributions that provide matching lower bounds, for every λ.