Analysis Of Lifetime Data Research Articles

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.

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.

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 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.

Analysis of the lifetime performance index in Gompertz distribution based on k-record values

The lifetime performance index plays a crucial role in manufacturing procedures as it provides valuable insights into the overall quality of a product. Considering the Gompertz distribution as a widely applicable statistical distribution, this index to emphasize the effect in analyzing lifetime data. This paper investigates the inference techniques associated with the lifetime performance index for the Gompertz distribution when k-record values are available. For this problem, two innovative methods are introduced utilizing the concept of the generalized pivotal variable. These methods are not only applicable to hypothesis tests but also enable the construction of confidence intervals. To further enhance the accuracy of estimation, the study proposes Bayesian estimation techniques based on the Metropolis–Hastings algorithms. To assess the efficacy of these methods, a simulation study is conducted. The results demonstrate that all three procedures exhibit exceptional performance, even when confronted with datasets consisting of small k-record values. Moreover, a dataset is utilized to demonstrate the implementation of these three methods.

On the effect of the Kaplan-Meier estimator’s assumed tail behavior on goodness-of-fit testing

When analyzing lifetime data in the presence of censoring one is often required to estimate the distribution function of the lifetimes non-parametrically. The most popular estimator used for this purpose is the Kaplan-Meier estimator. Interestingly, in its initial formulation this estimator is only defined up to the observed sample maximum. For values larger than the sample maximum two different assumptions are commonly used in the statistical literature. The first is to set the value of the estimate to one while the second is to use the value of the estimate at the sample maximum when estimating the tail of the distribution function. This paper illustrates the profound effect of these assumptions on the sizes and powers of goodness-of-fit tests for three classes of distributions often used in survival analysis. These differences are illustrated using observed remission time data. The considered classes of distributions are the exponential, Weibull and gamma. As a result of independent interest, we amend two classes of tests developed for the gamma distribution in the full sample case for use with censored data.

On ZLindley distribution: statistical properties and applications

The modeling and analysis of lifetime data is critical in many areas, including actuarial science, management, engineering, medicin, physics, biology, hydrology, and computer science. Classical probability distributions have been used to manage data sets of varied sizes. However, considerable issues occur when real-world data does not fit into any of the classical or conventional probability models. Consequently, there arises a crucial requirement to enhance the flexibility of existing probability models by including the blending of two distributions or introducing additional parameters. This work introduces a ZLindley distribution with a single parameter. Both symmetric and left-skewed data can utilize the proposed model. We generate statistical features such as the mode, moments, quantile function, and moment-generating function to accurately represent the usefulness of the suggested distribution. We compute the parameter using the maximum likelihood estimation approach. A thorough simulation exercise evaluates the goodness-of-fit performance. We demonstrate the applicability and flexibility of the new recommended distribution by using a real dataset.

Improving reliability system in radar model based on two parameters Weibull distribution

In this paper, the two parameters Weibull distribution lifetime model has been used to improve the reliability of a system in radar structure. This model is flexible to any lifetime data analysis and describing all stages of failure rate. Redundant and reduction methods of improving the system reliability are provided, including cold, hot, and imperfect methods. The lifetimes of units are assumed to be independent and non-identical components. To distinguish between different methods, we computed the mean time to failure and γ -fractiles. Reliability equivalence factors are also derived. Simulation examples were given to differentiate between different improving methods.

Evaluating the lifetime performance index of omega distribution based on progressive type-II censored samples

Besides achieving high quality products, statistical techniques are applied in many fields associated with health such as medicine, biology and etc. Adhering to the quality performance of an item to the desired level is a very important issue in various fields. Process capability indices play a vital role in evaluating the performance of an item. In this paper, the larger-the-better process capability index for the three-parameter Omega model based on progressive type-II censoring sample is calculated. On the basis of progressive type-II censoring the statistical inference about process capability index is carried out through the maximum likelihood. Also, the confidence interval is proposed and the hypothesis test for estimating the lifetime performance of products. Gibbs within Metropolis–Hasting samplers procedure is used for performing Markov Chain Monte Carlo (MCMC) technique to achieve Bayes estimation for unknown parameters. Simulation study is calculated to show that Omega distribution's performance is more effective. At the end of this paper, there are two real-life applications, one of them is about high-performance liquid chromatography (HPLC) data of blood samples from organ transplant recipients. The other application is about real-life data of ball bearing data. These applications are used to illustrate the importance of Omega distribution in lifetime data analysis.

On Estimation of Shannon’s Entropy of Maxwell Distribution Based on Progressively First-Failure Censored Data

Shannon’s entropy is a fundamental concept in information theory that quantifies the uncertainty or information in a random variable or data set. This article addresses the estimation of Shannon’s entropy for the Maxwell lifetime model based on progressively first-failure-censored data from both classical and Bayesian points of view. In the classical perspective, the entropy is estimated using maximum likelihood estimation and bootstrap methods. For Bayesian estimation, two approximation techniques, including the Tierney-Kadane (T-K) approximation and the Markov Chain Monte Carlo (MCMC) method, are used to compute the Bayes estimate of Shannon’s entropy under the linear exponential (LINEX) loss function. We also obtained the highest posterior density (HPD) credible interval of Shannon’s entropy using the MCMC technique. A Monte Carlo simulation study is performed to investigate the performance of the estimation procedures and methodologies studied in this manuscript. A numerical example is used to illustrate the methodologies. This paper aims to provide practical values in applied statistics, especially in the areas of reliability and lifetime data analysis.

Alpha power inverse Weibull distribution: A new lifetime distribution with application to gastric cancer data

Lifetime data analysis has an essential role in various fields of science. In general, lifetime data have a skewed distribution pattern. The Weibull distribution is one of the most frequently used distributions for modeling lifetime data. However, the Weibull distribution is not suitable for modeling data with non-monotonous hazard functions, one of which is an upside-down bathtub shape. According to Sharma et al. (2015), the inverse version of several probability distributions can model the data with an upside-down bathtub shape, one of which is the inverse Weibull distribution. This paper explains the Alpha Power Inverse Weibull (APIW) distribution as a generalization version of the inverse Weibull distribution. This distribution is constructed by using the Alpha Power Transformation method. The modification is done by adding a shape parameter to the inverse Weibull distribution to increase flexibility. The characteristics of APIW distribution discussed include probability density function, distribution function, survival function, hazard function, and the r-th moment. The probability density function of APIW distribution is left-skewed and unimodal. In addition, the hazard function of APIW distribution has an upside-down bathtub shape. The parameters of this distribution are estimated by the maximum likelihood method. Finally, for illustration purposes, the data about the time until gastric cancer patients die are modelled with the inverse Weibull distribution, and the APIW distribution is given. The modeling result shows that the Alpha Power Inverse Weibull distribution is better at modeling the time until gastric cancer patients die data than the inverse Weibull distribution.

A weighted Gompertz-G family of distributions for reliability and lifetime data analysis

This article is set to push new boundaries with leading-edge innovations in statistical distribution for generating up-to-the-minute contemporary distributions by a mixture of the second record value of the Gompertz distribution and the classical Gompertz model (weighted Gompertz model) using T-X characterization, especially used for two-sided schemes that provide an accurate model. The quantile, ordinary, and complete moments, order statistics, probability, and moments generating functions, entropies, probability weighted moments, Lin’s condition random variable, reliability in multicomponent stress strength system, reversed, and moments of residuals life and other reliability characteristics in engineering, actuarial, economics, and environmental technology were derived in their closed form. To investigate and test the flexibility, viability, tractability, and performance of the proposed Weighted Gompertz-G (WGG) generated model, the shapes of some sub-models of the WGG model were examined. The shapes of the sub-models indicated J-shapes, increasing, decreasing, and bathtub hazard rate functions. The maximum likelihood estimation of the WGG-generated model parameters was examined. An illustration with simulation and real-life data analysis indicated that the WGG-generated model provides consistently better goodness-of-fit statistics than some competitive models in the literature.

The odd log- logistic Power Inverse Lindley distribution: Model, Properties and Applications

In this article, we introduce a new three-parameter odd log-logistic power inverse Lindley distribution and discuss some of its properties. These include the shapes of the density and hazard rate functions, mixture representation, the moments, the quantile function, and order statistics. Maximum likelihood estimation of the parameters and their estimated asymptotic standard errors are derived. Three algorithms are proposed for generating random data from the proposed distribution. A simulation study is carried out to examine the bias and root mean square error of the maximum likelihood estimators of the parameters. An application of the model to three real data sets is presented finally and compared with the fit attained by some other well-known two and three-parameter distributions for illustrative purposes. It is observed that the proposed model has some advantages in analyzing lifetime data as compared to other popular models in the sense that it exhibits varying shapes and shows more flexibility than many currently available distributions.

A Generalized Additive Hazards Model for the Analysis of Lifetime Data

A Generalized Additive Hazards Model for the Analysis of Lifetime Data

Model misspecification of Log-Normal and Birnbaum-Saunders distributions

Model misspecification can be a serious issue in any lifetime data analysis. Assumption of the correct model is very important particularly in prediction for future observations and for estimating the tail probabilities of any lifetime distribution. In this paper we have considered the model misspecification of the log-normal and Birnbaum-Saunders distributions. These two distributions have striking similarities both in terms of the probability density functions and hazard functions, in certain range of parameter values, which makes it extremely difficult to detect the correct model. Hence, to identify the correct model, first the conventional method of ratio of maximized likelihood approach has been tried. The necessary theoretical results have been derived. Based on extensive simulations it has been observed that for certain range of parameter values the model misspecification can be quite high even for very large sample sizes. Some of the other methods like the ratio of maximized product of spacings and minimized Kolmogorov-Smirnov distance, have also been explored. But none of the method performs uniformly better than the other over the entire range of the parameter space. Some counter intuitive results have also been obtained. Hence, we finally conclude that it is extremely difficult to choose the correct model in case of log-normal and Birnbaum-Saunders distribution for certain range of parameter values. Finally, we have suggested a modified ratio of maximized likelihood approach, and the performances are quite satisfactory.

New Lifetime Distribution with Applications to Single Acceptance Sampling Plan and Scenarios of Increasing Hazard Rates

This article is an extension of the Chris-Jerry distribution (C-JD) in that a two-parameter Chris-Jerry distribution (TPCJD) is suggested and its characteristics are studied. Based on the determined domain of attraction and other major statistical properties, the proposed TPCJD seems to fit into the Gumbel domain. Additionally, it has been confirmed that the stress strength is reliable. The tail study suggests that the TPCJD’s substantial tail makes it suited for a range of applications. The study took into account the single acceptance sampling approach using both simulation and real-life situations. The parameters of the TPCJD were estimated by some classical and Bayesian approaches. The mean squared errors (MSE), linear-exponential, and generalized entropy loss functions were deployed to obtain the Bayesian estimators aided by the Markov chain Monte Carlo (MCMC) simulation. An analysis of lifetime data on two events justified the use of the proposed distribution after comparing the results with some standard lifetime models.

Semiparametric transformation model:A hierarchical Bayesian approach

The use of semiparametric or transformation models has been considered by many authors in the analysis of lifetime data in the presence of censoring and covariates as an alternative and generalization of the usual proportional hazards, the proportional odds models, and the accelerated failure time models, extensively used in lifetime data analysis. The inferences for the proportional hazards model introduced by Cox (1972) are usually obtained by maximum likelihood estimation methods assuming the partial likelihood function introduced by Cox (Cox, 1975). In this study, we consider a hierarchical Bayesian analysis of the proportional hazards model assuming the complete likelihood function obtained from a transformation model considering the unknown hazard function as a latent unknown variable under a Bayesian approach. Some applications with real time medical data illustrate the proposed methodology.

Retracted: The Neutrosophic Lognormal Model in Lifetime Data Analysis: Properties and Applications

Retracted: The Neutrosophic Lognormal Model in Lifetime Data Analysis: Properties and Applications

Heterometallic lanthanide complexes with site-specific binding that enable simultaneous visible and NIR-emission.

Macrocyclic lanthanide complexes have become widely developed due to their distinctive luminescence characteristics and wide range of applications in biological imaging. However, systems with sufficient brightness and metal selectivity can be difficult to produce on a molecular scale. Presented herein is the stepwise introduction of differing lanthanide ions in a bis-DO3A/DTPA scaffold to afford three trinuclear bimetallic [Ln2Ln'] lanthanide complexes with site-specific, controlled binding [(Yb2Tb), (Eu2Tb), (Yb2Eu)]. The complexes display simultaneous emission from all LnIII centers across the visible (TbIII, EuIII) and near infra-red (YbIII) spectrum when excited via phenyl ligand sensitization at a wide range of temperatures and are consequently of interest for exploiting imaging in the near infra-red II biological window. Analysis of lifetime data over a range of excitation regimes reveals intermetallic communication between TbIII and EuIII centers and further develops the understanding of multimetallic lanthanide complexes.

Comparison of phasor analysis and biexponential decay curve fitting of autofluorescence lifetime imaging data for machine learning prediction of cellular phenotypes.

Introduction: Autofluorescence imaging of the coenzymes reduced nicotinamide (phosphate) dinucleotide (NAD(P)H) and oxidized flavin adenine dinucleotide (FAD) provides a label-free method to detect cellular metabolism and phenotypes. Time-domain fluorescence lifetime data can be analyzed by exponential decay fitting to extract fluorescence lifetimes or by a fit-free phasor transformation to compute phasor coordinates. Methods: Here, fluorescence lifetime data analysis by biexponential decay curve fitting is compared with phasor coordinate analysis as input data to machine learning models to predict cell phenotypes. Glycolysis and oxidative phosphorylation of MCF7 breast cancer cells were chemically inhibited with 2-deoxy-d-glucose and sodium cyanide, respectively; and fluorescence lifetime images of NAD(P)H and FAD were obtained using a multiphoton microscope. Results: Machine learning algorithms built from either the extracted lifetime values or phasor coordinates predict MCF7 metabolism with a high accuracy (∼88%). Similarly, fluorescence lifetime images of M0, M1, and M2 macrophages were acquired and analyzed by decay fitting and phasor analysis. Machine learning models trained with features from curve fitting discriminate different macrophage phenotypes with improved performance over models trained using only phasor coordinates. Discussion: Altogether, the results demonstrate that both curve fitting and phasor analysis of autofluorescence lifetime images can be used in machine learning models for classification of cell phenotype from the lifetime data.