Lifetime Data Research Articles

Nonparametric Predictive Inference for Discrete Lifetime Data

This paper presents nonparametric predictive inference for discrete lifetime data. While lifetimes are mostly treated as continuous random variables in statistics, there are scenarios where time observations are recorded as discrete values, for example, in actuary, where lifetimes are often recorded as integers in years. The presented method provides lower and upper probabilities for a variety of events of interest involving discrete lifetimes, with examples provided for illustration. Furthermore, the discrete-time situation is considered for inference of the reliability of systems, with discrete-time data for components of different types and using the survival signature to combine inference on components’ reliability to quantify the overall system reliability.

THE ODD LOMAX TOPP LEONE DISTRIBUTION: PROPERTIES AND APPLICATION

Lifetime distributions are parametric models used in statistical analyses of time-to-event data. Several probability distributions have been very used in literature to model lifetime data sets which have been useful in the analysis of lifetime data, but in most cases, they are not flexible enough to analyze some complex lifetime data in practice. Due to the importance of these lifetime distributions in modeling real lifetime data, there has several modifications and generalization of lifetime distributions, particularly the Lomax distribution to develop more flexible distributions to address the drawback presented by some classical lifetime distributions including the Lomax distribution. Several attempts have been made by researchers to generalize classical lifetime distributions which offer more flexibility in modeling lifetime data. Our interest in this study is to introduce a new extension of Lomax distribution called the “The odd lomax Topp-Leone distribution” which is bounded on a unit interval data such that its flexibility can accommodate increasing, decreasing, right skewed, left skewed, symmetric and u-shaped data sets. An application to a real lifetime data set clearly shows that the proposed extension of the Lomax distribution is a better alternative to some existing distributions bounded on a unit interval.

Two-stage pseudo maximum likelihood estimation of semiparametric copula-based regression models for semi-competing risks data.

We propose a two-stage estimation procedure for a copula-based model with semi-competing risks data, where the non-terminal event is subject to dependent censoring by the terminal event, and both events are subject to independent censoring. With a copula-based model, the marginal survival functions of individual event times are specified by semiparametric transformation models, and the dependence between the bivariate event times is specified by a parametric copula function. For the estimation procedure, in the first stage, the parameters associated with the marginal of the terminal event are estimated using only the corresponding observed outcomes, and in the second stage, the marginal parameters for the non-terminal event time and the copula parameter are estimated together via maximizing a pseudo-likelihood function based on the joint distribution of the bivariate event times. We derived the asymptotic properties of the proposed estimator and provided an analytic variance estimator for inference. Through simulation studies, we showed that our approach leads to consistent estimates with less computational cost and more robustness than the one-stage procedure developed in Chen YH (Lifetime Data Anal 18:36-57, 2012), where all parameters were estimated simultaneously. In addition, our approach demonstrates more desirable finite-sample performances over another existing two-stage estimation method proposed in Zhu H et al., (Commu Statistics-Theory Methods 51(22):7830-7845, 2021) . An R package PMLE4SCR is developed to implement our proposed method.

Statistical analysis for progressive stress accelerated life test with transmutation Weibull distribution

The Transmutation Weibull distribution is derived from the quadratic rank transmutation map of the Weibull distribution. This distribution integrates the high adaptability of the Weibull distribution in engineering and materials fields, and has great potential utility for modeling lifetime data. Therefore, the article explores the progressive stress accelerated life test model for components under the Transmutation Weibull distribution, conducts statistical analysis using the maximum likelihood estimation (MLE), Lindley’s approximation, and Markov Chain Monte Carlo (MCMC) algorithm to provide approximate estimates for the model. Finally, by comparing the results of numerical simulations, it is confirmed that the Bayesian estimation is more accurate and effective.

Multivariate lifetime data in presence of censoring and covariates: Use of semiparametric models under a Bayesian approach

A generalization of the popular proportional hazards model introduced by Cox (1972) is given by the class of semiparametric or transformation models to be used in the analysis of lifetime data in presence of censored data and covariates. In this study, we consider the use of semiparametric (transformation models) for the situation where there are two or more responses associated to the same individual or unit. We assume a hierarchical Bayesian analysis for semiparametric models considering the complete likelihood function obtained from the transformation models considering the unknown hazard functions as unknown latent variables and Markov Chain Monte Carlo (MCMC) methods to get the posterior summaries of interest. The dependence between multivariate responses for the same individual is captured by the introduction of another latent variable or frailty. Illustrations of the proposed methodology are presented considering two medical multivariate lifetime data sets.

Hanle Effect for Lifetime Determinations in the Soft X-Ray Regime.

By exciting a series of 1s^{2} ^{1}S_{0}→1snp^{1}P_{1} transitions in heliumlike nitrogen ions with linearly polarized monochromatic soft x rays at the Elettra facility, we found a change in the angular distribution of the fluorescence sensitive to the principal quantum number n. In particular it is observed that the ratio of emission in directions parallel and perpendicular to the polarization of incident radiation increases with higher n. We find this n dependence to be a manifestation of the Hanle effect, which served as a practical tool for lifetime determinations of optical transitions since its discovery in 1924. In contrast to traditional Hanle effect experiments, in which one varies the magnetic field and considers a particular excited state, we demonstrate a "soft x-ray Hanle effect" which arises in a static magnetic field but for a series of excited states. By comparing experimental data with theoretical predictions, we were able to determine lifetimes ranging from hundreds of femtoseconds to tens of picoseconds of the 1snp^{1}P_{1} levels, which find excellent agreement with atomic-structure calculations. We argue that dedicated soft x-ray measurements could yield lifetime data that are beyond current experimental reach and cannot yet be predicted with sufficient accuracy.

A New Lifetime Distribution and its Application to Cancer Data

Introduction: Recently, researchers have introduced new generated families of univariate lifetime distributions. These new generators are obtained by adding one or more extra shape parameters to the underlying distribution or compounding two distributions to get more flexibility in fitting data in different areas such as medical sciences, environmental sciences, and engineering. The addition of parameter(s) has been proven useful in exploring tail properties and for improving the goodness-of-fit of the family of the proposed distributions. Methods:A new Three-Parameter Weibull-Generalized Gamma distribution which provides more flexibility in modeling lifetime data is developed using a two-component mixture of Weibull distribution (with parameters θ and λ) and Generalised Gamma distribution (with parameters α=4,θ and λ). Some of its mathematical properties such as the density function, cumulative distribution function, survival function, hazard rate function, moment generating function, Renyi entropy and order statistics are obtained. The maximum likelihood estimation method was used in estimating the parameters of the proposed distribution and a simulation study is performed to examine the performance of the maximum likelihood estimators of the parameters. Results: Real life applications of the proposed distribution to two cancer datasets are presented and its fit was compared with the fit attained by some existing lifetime distributions to show how the Three-Parameter Weibull-Generalized Gamma distribution works in practice Conclusion: The results suggest that the proposed model performed better than its competitors and it’s a useful alternative to the existing models.

A Generalized Suja Distribution with Application to Lifetime Data

This paper introduces a generalized Suja distribution called the Kumaraswamy-Suja (KW-Suja) distribution using the Kumaraswamy generator. The proposed distribution has Suja distribution as a special case. Some statistical and reliability properties of the new distribution were derived and the method of maximum likelihood was employed for estimating the model parameters. The usefulness and flexibility of the KW-Suja distribution were illustrated with a real lifetime data. Results based on the log-likelihood and goodness of fit statistics values showed that the KW-Suja distribution provides a better fit to the data than the other competing distributions considered in this study. The KW-Suja distribution is therefore recommended for effective modelling of the unimodal or bimodal continuous lifetime data with non-decreasing shape and bathtub-shaped failure rate.

Variants of Mutual Arrangement of Parts of Human Pancreas According to Computed Tomography Data

INTRODUCTION: With development of methods of diagnosis and surgical treatment of diseases of hepatopancreato-biliary region, there is increasing interest in and necessity to search for various methods of studying organs of this zone. Compared to the earlier methods of studying topographic anatomy, the method of computed tomography (KT) permits to work with a wide scope of lifetime data of human anatomy. We did not find enough information in the literature about peculiarities of the shape, size and position of pancreas in the horizontal projection. AIM: To study the peculiarities of the shape, size and position of the pancreas using contrast-enhanced CT data. MATERIALS AND METHODS: The work was based on the available archive of examination of organs of the abdominal cavity by CT method with contrast in patients (n = 31) without pathology of the hepatopancreatobiliary zone, gastrointestinal tract, spleen, kidneys and spine. Measurements were performed based on the horizontal projection of scans. The length was determined by measuring the organ in parts. The degree of curvature of the pancreas shape was determined by constructing the central axis of the organ and measuring the angles formed by it. The obtained data were subjected to statistical processing. RESULTS: According to increase in the length of the organ, three groups were formed. Different degrees of the organ bending were identified. Upon that, no clear correlation was found with skeletopy data, age and gender and parametric data of the upper part of the abdominal cavity. CONCLUSION: Owing to the developed method of measuring angles between parts of the pancreas, a range of mutual arrangement of the head and body, body and tail of the gland in the horizontal projection was obtained. Our data complement the anatomy of the pancreas and can be considered as a promising resource for further study of the features of syntopy and blood supply of the organs of the upper part of the abdominal cavity.

Repair alert model when the lifetimes are discretely distributed

This paper deals with the repair alert models. They are used for analyzing lifetime data coming from engineering devices under maintenance management. Repair alert models have been proposed and investigated for continuous component lifetimes. Existing studies are concerned with the lifetimes of items described by continuous distributions. However, discrete lifetimes are also frequently encountered in practice. Examples include operating a piece of equipment in cycles, reporting field failures that are gathered weekly, and the number of pages printed by a device completed before failure. Here, the repair alert models are developed when device lifetimes are discrete. A wide class of discrete distributions, called the telescopic family, is considered for the component lifetimes, and the proposed repair alert model is explained in detail. Furthermore, the problem of estimating parameters is investigated and illustrated by analyzing a real data set.

A new extension of Burr-Hatke exponential distribution with engineering and biomedical applications

In this study, the Topp-Leone family of distribution approach was used to modify the Burr Hatke Exponential distribution to provide adequate fits for some engineering and health data which previous existing distributions in the family of Burr Hatke Exponential have failed to do. The new distribution improves the robustness of Burr Hatke Exponential distribution by making it capable of modeling emerging new world complex data with varying features, possesses greater capacity and flexibility to model lifetime data, has better goodness of fit. Some mathematical properties of the derived distribution such as quantile function, moments, order statistics, entropies, etc were obtained and discussed. Some non-Bayesian estimation approaches like maximum likelihood estimation (ML), maximum Product spacing estimation (MPSE), Least squares estimation (LS), weighted least squares estimation (WLS), Cramer-von-Mises estimation (CVM), Anderson-Darling estimation (AD), and right-tailed Anderson Darling estimation (RTAD), as well as Bayesian method under independent gamma priors were adopted to estimate the parameters of the model and the various methods proved efficient. From the simulation results, the bias and root mean squared error for the parameters are relatively small and the become smaller as the sample size becomes larger. This shows convenience and improved estimation accuracy. We further constructed a regression model using the proposed distribution. Extensive simulation studies were used to determine the efficiency of the method in both the estimation of its parameters and that of the regression model. The TL-BHE regression was fitted on censored CD4 count data of HIV/AIDs patients. The competitiveness, applicability, and usefulness of the model were demonstrated using datasets and the results validate the theoretical findings. The results indicate that the TL-BHE distribution achieved better results than the baseline distribution and other variants of the classical distributions.

A Novel Technique for Fluorescence Lifetime Tomography.

Fluorescence lifetime has emerged as a unique imaging modality for quantitatively assessing in vivo the molecular environment of diseased tissues. Although fluorescence lifetime microscopy (in 2D) is a mature field, 3D imaging in deep tissues remains elusive and challenging owing to scattering. Herein, we report on a deep neural network (coined AUTO-FLI) that performs both 3D intensity and quantitative lifetime reconstructions in deep tissues. The proposed Deep Learning (DL)-based approach involves an in silico scheme to generate fluorescence lifetime data accurately. The developed DL model is validated both in silico and on experimental phantoms. Overall, AUTO-FLI provides accurate 3D quantitative estimates of both intensity and lifetime distributions in highly scattering media, demonstrating its unique potential for fluorescence lifetime-based molecular imaging at the mesoscopic and macroscopic scale.

Optimized Wireless Visual Sensor Networks for Guaranteed Target Coverage With Maximum Lifetime and Least Data Delivery Latency

Optimized Wireless Visual Sensor Networks for Guaranteed Target Coverage With Maximum Lifetime and Least Data Delivery Latency

Bayesian reliability estimation of weighted exponential-lindley distribution with intuitionistic fuzzy lifetime data

Bayesian reliability estimation of weighted exponential-lindley distribution with intuitionistic fuzzy lifetime data

A distribution-free method for reliability improvement based on design of experiments

Given growing consumer expectations for enhanced product lifespans, there is a particular focus on improving product reliability. Design of Experiments (DOE) is a useful tool for identifying significant factors and determining factor levels to enhance product reliability. Current research commonly assumes that the lifetime data follows a specific distribution. This overlooks the possibility that erroneous assumptions about the data distribution may lead to imprecise factors identification. Additionally, factorial effect principles are often disregarded in factors effects identification. In this paper, a distribution-free method named Factor-Effect Bayesian Quantile Regression (FEBQR) is proposed to address the aforementioned issues. We first construct a new set of factor indicator variables, considering the principles of effect sparsity, weak effect hierarchy, and effect heredity. Then we develop a novel model that extends the Bayesian quantile regression framework by incorporating the principle of factor effects to describe the relationship between percentile lifetimes and factor effects. Unknown parameter estimates are obtained through the Gibbs sampling algorithm, and significant factors are identified based on the posterior mean of the proposed factor indicator variables. Two practical examples are illustrated using the proposed method. Compared with traditional methods, the proposed method provides more accurate factor identification results.

A new two-parameter Rayleigh distribution: Statistical properties, actuarial measures, regression analysis, and applications

This paper presents a novel two-parameter distribution derived from the Rayleigh distribution, thoroughly investigating its essential mathematical properties. We employ estimation techniques to determine the proposed distribution's estimated parameters. Through extensive simulation studies, we analyze and evaluate the asymptotic behavior of the model estimators. Furthermore, we calculate various actuarial measures to highlight the practical utility of the proposed distribution in actuarial science. To further substantiate the applicability of our distribution, we perform a comprehensive regression analysis. The practical relevance of the proposed distribution is demonstrated by modeling a lifetime dataset from the insurance field, where it exhibits a superior fit compared to existing distributions. The findings suggest that the new distribution significantly improves modeling capabilities, making it a valuable tool for theoretical research and practical applications in fields requiring accurate lifetime data modeling.

The promise and peril of comparing fluorescence lifetime in biology revealed by simulations.

Signaling dynamics are crucial in biological systems, and biosensor-based real-time imaging has revolutionized their analysis. Fluorescence lifetime imaging microscopy (FLIM) excels over the widely used fluorescence intensity imaging by allowing the measurement of absolute signal levels, independent of sensor concentration. This capability enables the comparison of signaling dynamics across different animals, body regions, and timeframes. However, FLIM's advantage can be compromised by factors like autofluorescence in biological experiments. To address this, we introduce FLiSimBA, a flexible computational framework for realistic F luorescence Li fetime Sim ulation for B iological A pplications. Through simulations, we analyze the signal-to-noise ratios of fluorescence lifetime data, determining measurement uncertainty and providing necessary error bars for lifetime measurements. Furthermore, we challenge the belief that fluorescence lifetime is unaffected by sensor expression and establish quantitative limits to this insensitivity in biological applications. Additionally, we propose innovations, notably multiplexed dynamic imaging that combines fluorescence intensity and lifetime measurements. This innovation can transform the number of signals that can be simultaneously monitored, thereby enabling a systems approach in studying signaling dynamics. Thus, by incorporating diverse factors into our simulation framework, we uncover surprises, identify limitations, and propose advancements for fluorescence lifetime imaging in biology. This quantitative framework supports rigorous experimental design, facilitates accurate data interpretation, and paves the way for technological advancements in fluorescence lifetime imaging.

Gamma–lindley regression cure model for corporate credit default prediction

Predicting the firm’s default over time is marked persistently with certain flaws for firms seeking to avoid their exposure to credit risk and losses induced by defaults. From this perspective, a Gamma–lindley cure model, relying on a Gamma–lindley distribution and the survival analysis framework, was introduced to model the default probability and time of corporate credits referring to their inference ability once the firm is likely to default. In addition, it extends the standard mixture cure model allowing more flexibility for modeling lifetime data through relaxing the independence assumption of the probability and the time of default. Furthermore, it handles the missing defaulting labels as a latent variable and identifies three classes of default probability distribution, namely short, medium, and long-term through its potentially accurate classification method. A relevant parameter-learning procedure was described resting on the Maximum Likelihood approach. The results of an empirical analysis on a firms dataset reveal that the advanced Gamma–lindley cure model has a rather effective performance in terms of default time prediction compared to Exponential, Gamma, Weibull, and Cox proportional hazards regression modeling specifications, which yield a meaningful solution for timely credit risk management and cluster firms defaulter in three classes, enabling a deeper analysis of firm’s defaults situation. The numerical experiments were conducted with Python language.

A New Generalization of the Inverse Generalized Weibull Distribution with Different Methods of Estimation and Applications in Medicine and Engineering

Limitations inherent to existing statistical distributions in capturing the complexities of real-world data often necessitate the development of novel models. This paper introduces the new exponential generalized inverse generalized Weibull (NEGIGW) distribution. The NEGIGW distribution boasts significant flexibility with symmetrical and asymmetrical shapes, allowing its hazard rate function to be adapted to many failure patterns observed in various fields such as medicine, biology, and engineering. Some statistical properties of the NEGIGW distribution, such as moments, quantile function, and Renyi entropy, are studied. Three methods are used for parameter estimation, including maximum likelihood, maximum product of spacing, and percentile methods. The performance of the estimation methods is evaluated via Monte Carlo simulations. The NEGIGW distribution excels in its ability to fit real-world data accurately. Five medical and engineering datasets are applied to demonstrate the superior fit of NEGIGW distribution compared to competing models. This compelling evidence suggests that the NEGIGW distribution is promising for lifetime data analysis and reliability assessments across different disciplines.

Next-generation statistical methodology: Advances health science research

Accurately modeling health science data is crucial for advancing medical research and improving patient outcomes. Traditional statistical analysis methods face significant challenges due to the complexity and diversity of health sciences data. This article introduces a groundbreaking statistical framework designed to overcome these challenges by developing a next-generation family of distributions, with a special focus on the versatility of the Weibull distribution. The data used in this study has been thoroughly authenticated to ensure reliability and validity. Comprehensive Monte Carlo simulations revealed that the Maximum Product of Spacing Estimator is the most effective among seven-point estimation methods, according to standard metrics. Additionally, the study identifies optimal methods for analyzing various types of lifetime data, including the Maximum Product of Spacing Estimator for pharmaceutical efficacy (ED50), the Least Squares Estimator for psychiatric treatment durations, the Cramer-von Mises Estimator for data on 43 leukemia patients and for survival periods of 20 leukemia patients, and the Right Tail Anderson-Darling Estimator for remission times of 128 bladder cancer patients. The adaptability and flexibility of the next-generation Weibull distribution set it apart as the best match among its contemporaries.