Hazard Rate Model Research Articles

Dynamic version of past inaccuracy measure under PRHR model based on extropy

This article investigates the concept of a past inaccuracy measure and its dynamic version. The properties of this measure are studied and the discrimination principle is applied to obtain the proportional reversed hazard rate (PRHR) model. Under the assumption that the reference distribution and true distribution satisfy the PRHR model, it has been shown that the proposed measure determines the lifetime distribution uniquely. Furthermore, the provided measure of inaccuracy is demonstrated to be invariant on scale transformation but not on location transformation. We propose some alternative expressions of the dynamic past measure of inaccuracy. A study is conducted on a characterization problem for the suggested extropy inaccuracy measure. Additionally, several inequalities and upper and lower bounds for the extropy-based dynamic past inaccuracy measure are established. Moreover, a simulation study is used to evaluate the performance of kernel-based non parametric estimators for the suggested measure. Finally, an application for model selection based on the proposed measure is provided.

Transmuted Unit Exponentiated Half-Logistic Distribution and its Applications

A novel distribution, termed the transmuted unit exponentiated half-logistic distribution, was proposed using the unit exponential half-logistic distribution, a member of the proportional hazard rate model family, as the base distribution. The statistical characteristics of the proposed distribution, including moments, moment-generating function, quantile function, and stress-strength reliability, were thoroughly examined in this study. The maximum likelihood estimation method is discussed for statistical inference of the distribution parameters. A simulation study based on the new distribution was conducted to investigate the behavior of maximum likelihood estimates under various conditions. In addition, a numerical example is presented to illustrate the performance of the distribution on a failure-time dataset.

Residual Inaccuracy Extropy and its properties

Abstract In this paper, we introduce a novel concept of a dynamic residual inaccuracy measure based on extropy. We extend the traditional residual inaccuracy measure to its dynamic version, which allows us to measure the discrepancy between two residual life distributions. We study the properties of the proposed measure, including its discrimination principle and the proportional hazard rate model. We also investigate a characterization problem related to the extropy inaccuracy measure and propose some alternative expressions of the dynamic residual measure of inaccuracy. Furthermore, we establish upper and lower bounds and some inequalities concerning dynamic residual inaccuracy measures based on extropy. We demonstrate that the defined measure of inaccuracy is invariant under scale but not under location transformation. The given findings have important implications for statistical inference, estimation, and modeling. The proposed extropy-based dynamic residual inaccuracy measure provides a powerful tool for quantifying the discrepancy between two residual life distributions over time. At the end of the paper, we provide two non-parametric estimators for the proposed extropy measure of inaccuracy for both the non-censored (complete sample) and the right-censored scheme. The performances of these estimators are compared numerically based on their bias and MSE.

Availability modeling of competing risk system with multiple failure modes incorporating hybrid hazard rate model

Availability modeling of competing risk system with multiple failure modes incorporating hybrid hazard rate model

Compromises in occupational choice and premature termination of vocational education and training: gender type, prestige, and occupational interests in focus

This study examines whether premature termination of vocational education and training (VET) is more likely when trainees have to make compromises between their realistic occupational aspirations and the occupation for which they are trained in terms of the occupational dimensions of gender type, prestige, and occupational interests. Specifically, it examines the relative importance of the three compromise dimensions on premature VET termination. The study is based on a sample of 3,241 VET entrants from a cohort of ninth graders in 2010 in the German National Educational Panel Study (NEPS-SC4) in combination with aggregated data on occupational characteristics. Results from discrete hazard rate models indicate a higher risk of premature VET termination for trainees whose VET occupation differs from their realistic occupational aspiration from their school days. While compromises in prestige have no overall effect, both compromises in interests and gender type threaten the stability of VET. The results also indicate that compromises in interests have the strongest effect on the risk of premature VET termination and that the effects of compromises in gender type are partly mediated by the effects of compromises in interests. Furthermore, sensitivity analysis revealed that the main effects of compromises in gender type and prestige are gender specific.

Some stochastic comparison results for frailty and resilience models

. Frailty and resilience models provide a way to introduce random effects in hazard and reversed hazard rate modeling by random variables, called frailty and resilience random variables, respectively, to account for unobserved or unexplained heterogeneity among experimental units. This article investigates the effects of frailty and resilience random variables on the baseline random variables using some shifted stochastic orders based on some ageing properties of the baseline random variables. Relevant examples are presented to illustrate the findings, and the applicability of the results is demonstrated with real-world data, highlighting their relevance in practical scenarios.

Inference Based on Sequential Order Statistics with Lindley Distribution

In this paper, we consider the problem of estimation of parameters of Lindley distribution based on sequential order statistics under conditional proportional hazard rate model. Maximum Likelihood and Bayesian estimation techniques are applied for estimating the unknown parameters. Markov Chain Monte Carlo method is implemented for obtaining the Bayes estimators. An intensive simulation study is carried out to assess the performance of different estimators discussed in this paper. A real data analysis is also performed for illustrative purposes.

The generalized order statistics arising from three populations with the lower truncated proportional hazard rate models and its application to the sensitivity to the early disease stage

ABSTRACT In this paper, we present some results to make inference about the parameters of lower truncated proportional hazard rate models with the same baseline distributions based on three independent generalized order statistics samples. Then, especially by considering the results of the diagnostic tests for the non-diseased, early-diseased stage and fully diseased populations, we make inference about sensitivity to the early disease stage parameter. The maximum likelihood estimator, a generalized pivotal estimator and some Bayes estimators are obtained for different structures of prior distributions. The percentile bootstrap confidence interval, a generalized pivotal confidence interval and some Bayesian credible intervals are also presented. A Monte Carlo simulation study is used to evaluate the performances of the obtained point estimators and confidence/credible intervals and two competitors. We use two real datasets to illustrate the proposed methods.

Energy-based availability warranty policy with considering preventive maintenance and learning-forgetting effect

Ensuring reliable operation and maximum the output is crucial for energy production systems. Traditional time-based availability (TBA) warranty policies often overlook some factors, such as energy loss and the experience gained during the maintenance activities. In this paper, an innovative warranty policy which focuses on the energy-based availability (EBA) is proposed, where imperfect preventive maintenance (IPM) and minimal repair (MR) are taken into account, and hybrid hazard rate model is adopted to describe the effect of preventive maintenance. In addition, the learning-forgetting effect during the maintenance is considered. On this basis, six types of single-objective and multi-objective models are established, and they are solved by genetic algorithm (GA) and non-dominated sorting genetic algorithm-II (NSGA-II), respectively. To illustrate the effectiveness of the proposed warranty policy, a numerical case of wind turbine gearbox is conducted. The results show that the proposed EBA warranty policy can gain around 0.29% energy more than TBA policy. Compared to single-objective models, multi-objective models can provide more selectable maintenance options. Additionally, sensitivity analysis indicates that by considering the learning-forgetting effect, the gearbox can achieve higher EBA and lower warranty cost.

Climate change, tipping points, and economics

This paper discusses the response of the economics profession to a possible occurrence of tipping points in natural systems, with a drop in welfare. For a climate tipping point, the hazard-rate model is relevant, and the paper shows that in a Ramsey growth model with climate tipping, the effect on policy is increased saving and increased taxation of greenhouse gas emissions. Climate change is often seen as a tragedy of the commons because incentives to deviate undermine cooperation and prevention of climate change. However, a climate tipping point can be prevented in a Nash equilibrium or with partial cooperation if the drop in welfare is sufficiently high. In case of uncertainty about the threshold, this result remains if the uncertainty is not too large. In the conclusion, the paper makes a few remarks on including tipping points in teaching environmental and resource economics.

Weighted (residual) varentropy and its applications

In information theory, it is of recent interest to study variability of the uncertainty measures. In this regard, the concept of varentropy has been introduced and studied by several authors in recent past. In this communication, we study the weighted varentropy and weighted residual varentropy. Several theoretical results of these variability measures such as the effect under monotonic transformations and bounds are investigated. Importance of the weighted residual varentropy over the residual varentropy is presented. Further, we study weighted varentropy for coherent systems and weighted residual varentropy for proportional hazard rate models. A kernel-based non-parametric estimator for the weighted residual varentropy is also proposed. The estimation method is illustrated using simulated and two real data sets.

A new two-parametric weighted generalized inaccuracy measure

Abstract In this article, we present a novel approach to measuring inaccuracy, introducing a two-parametric weighted generalized inaccuracy measure of order α and type β, along with its residual version. Our proposed measure depends on the proportional hazard rate model (PHRM) to uniquely determine the survival function, and we have derived a characterization result for this measure. Through our analysis under the PHRM framework, we have studied various properties of the proposed measure and their interrelationships.

Relative Orderings of Modified Proportional Hazard Rate and Modified Proportional Reversed Hazard Rate Models

In this paper, we identify several relative ordering properties of the modified proportional hazard rate and modified proportional reversed hazard rate models. For this purpose, we use two well-known relative orderings, namely the relative hazard rate ordering and the relative reversed hazard rate ordering. The investigation is to see how a relative ordering between two possible base distributions for the response distributions in these models is preserved when the parameters of the underlying models are changed. We will give some examples to illustrate the results and the conditions under which they are obtained. Numerical simulation studies have also been provided to examine the examples presented.

Statistical inference for the partial area under ROC curve for the lower truncated proportional hazard rate models based on progressive Type-II censoring

This paper considers inference on the partial area under the receiver operating characteristic curve based on two independent progressively Type-II censored samples from the populations that are belonging to the lower truncated proportional hazard rate models with the same baseline distributions. The maximum likelihood estimator, a generalized pivotal estimator and some Bayes estimators are obtained for three structures of prior distributions. The percentile bootstrap confidence interval, a generalized pivotal confidence interval and some Bayesian credible intervals are also presented. A Monte-Carlo simulation study is used to evaluate the performances of the obtained point estimators and confidence and credible intervals. Finally, a real data set is applied for illustrative purposes.

Multilatinas’ foreign divestment and host country institutional uncertainty: is there a best entry strategy?

PurposeThis paper aims to investigate the divestment behavior of emerging market multinationals from Latin America – multilatinas – by examining how their foreign market entry decision impacts the likelihood of subsidiary divestment.Design/methodology/approachThe hypotheses are tested using Cox’s proportional hazard rate model in a longitudinal database of Brazilian multinational companies established in 43 countries.FindingsResults indicate that these subsidiaries can thrive in environments that bear similarities to their home country, being less likely to divest in institutionally weak countries. Contrary to developed country multinationals, these firms benefit from foreign entry decisions that entail handling partnerships abroad; thus, wholly-owned greenfield (WOGF) investments have a higher likelihood of being divested.Originality/valueTo the best of the authors’ knowledge, this paper is the first to analyze foreign divestment from multilatinas, accounting for how entry mode strategy and host country institutions may impact these firms’ de-internationalization.

Framing your concerns right: an analysis of air passengers' complaints during two time periods

PurposeConsumers are increasingly choosing social media over other channels and mechanisms for grievance redressal. However, not all social media grievances elicit a response from businesses. Hence, in this research the authors aim to explore the effect of the complainant's social characteristics and the complaint's social and content characteristics on the likelihood of receiving a response to a grievance from the business on social media.Design/methodology/approachThe authors build a conceptual model and then empirically test it to explore the effect of the complainant's characteristics and the complaint's characteristics on the likelihood of response from a business on social media. The authors use data of consumer grievances received by an Indian airline operator on Twitter during two time periods – the first corresponding to lockdown during Covid-19 pandemic, and the second corresponding to the resumption of business as usual following these lockdowns. The authors use logistic regression and the hazard rate model to model the likelihood of response and the response delay, respectively, for social media customer grievances.FindingsComplainants with high social influence are not more likely to get a response for their grievances on social media. While tagging other individuals and business accounts in a social media complaint has negative effect on the likelihood of business response in both the time periods, the effect of tagging regulatory bodies on the likelihood of response was negative only in the Covid-19 lockdown period. The readability and valence of a complaint were found to positively affect the likelihood of response to a social media grievance. However, the effect of valence was significant only in lockdown period.Originality/valueThis research offers insights on what elicits responses from a service provider to consumers' grievances on social media platforms. The extant literature is a plenty on how firms should be engaging consumers on online media and how online communities should be built, but scanty on grievance redressal on social media. This research is, therefore, likely to be useful to service providers who are inclined to improve their grievance handling mechanisms, as well as, to regulatory authorities and ombudsmen.

Cumulative α-Jensen–Shannon measure of divergence: Properties and applications

The problem of quantifying the distance between distributions arises in various fields, including cryptography, information theory, communication networks, machine learning, and data mining. In this article, the analogy with the cumulative Jensen–Shannon divergence, defined in Nguyen and Vreeken (2015), we propose a new divergence measure based on the cumulative distribution function and call it the cumulative α-Jensen–Shannon divergence, denoted by CJS ( α ) . Properties of CJS ( α ) are studied in detail, and also two upper bounds for CJS ( α ) are obtained. The simplified results under the proportional reversed hazard rate model are given. Various illustrative examples are analyzed.

Estimation of Reliability in Multicomponent Set-up when Stress and Strength are Non-identical

In the multicomponent stress–strength reliability literary work, though assumption of identical stress and strengths components may not be universally true but have been commonly considered. Herein, we consider a multicomponent stress–strength model having k identical strength components, say X_i,~i=1,2,...,k, which are exposed to a common random stress Y, so that Y, X_i,~i=1,2,...,k are independent. Two different generalized cases of estimation are considered; namely, (i) when the strength components follow the proportional hazard rate model and stress component follows the proportional reversed hazard rate model and (ii) when the strength components follow the proportional reversed hazard rate model and stress component follow the proportional hazard rate model. In each case, maximum likelihood and Bayesian approach using Markov Chain Monte Carlo method has been utilized to estimate the reliability of the system. Asymptotic confidence intervals are also constructed for the reliability functions in both the cases. Monte Carlo simulation study is exercised to compare the performance of the aforementioned estimators. A real data example is also explored to examine the utility of the paper.

Pricing credit-risky bonds using recovery rate uncertainty and macro-regime switching

A proposed model is used to account for both the recovery rate and regime-switching uncertainties for pricing credit-risky bonds. A two-factor hazard rate model (TFHRM) is also considered, where the dynamics of both instantaneous forward rates and asset values are modeled using Markov-modulated geometric Brownian motions (MMGBMs). Moreover, a macroeconomic factor is incorporated into the MMGBMs. The model complexity is resolved through the introduction of an endogenous intensity function and a recovery rate under the TFHRM. A semi-closed-form solution for pricing defaultable bonds is derived along with a pricing formula for credit spread. A credit cycle is constructed to reflect changes in industry characteristics and macroeconomic factors. The empirical study demonstrates that the inclusion of a stochastic recovery rate increases the model’s pricing accuracy, and the results indicate a close interaction among business cycles, recovery rates, and credit ratings.

Time-dependent event accumulation in a cardiovascular outcome trial of patients with type 2 diabetes and established atherosclerotic cardiovascular disease

BackgroundEstimating cardiovascular (CV) event accrual is important for outcome trial planning. Limited data exist describing event accrual patterns in patients with type 2 diabetes (T2D). We compared apparent CV event accrual patterns with true event rates in the Trial Evaluating Cardiovascular Outcomes with Sitagliptin (TECOS).MethodsCentrally adjudicated event dates and accrual rates for a 4-point major adverse CV event composite (MACE-4; includes CV death, nonfatal myocardial infarction, nonfatal stroke, or unstable angina hospitalization), MACE-4 components, all-cause mortality (ACM), and heart failure hospitalization were compiled. We used three graphical methods (Weibull probability plot, plot of negative log of the Kaplan–Meier survival distribution estimate, and the Epanechnikov kernel-smoothed estimate of the hazard rate) to examine hazard rate morphology over time for the 7 outcomes.ResultsPlots for all outcomes showed real-time constant event hazard rates for the duration of the follow-up, confirmed by Weibull shape parameters. The Weibull shape parameters for ACM (1.14, 95% CI 1.08–1.21) and CV death (1.08, 95% CI 1.01–1.16) were not sufficiently > 1 as to require non-constant hazard rate models to accurately depict the data. The time lag between event occurrence and event adjudication being completed, the adjudication gap, improved over the course of the trial.ConclusionsIn TECOS, the nonfatal event hazard rates were constant over time. Small increases over time in the hazard rate for fatal events would not require complex modelling to predict event accrual, providing confidence in traditional modelling methods for predicting CV outcome trial event rates in this population. The adjudication gap provides a useful metric to monitor within-trial event accrual patterns.Clinical trial registrationClinicaltrials.gov NCT00790205.