Lifetime Data Sets 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.

Physical aspects of quantile residual lifetime sequence

Abstract The modeling of count data is found in many fields, such as statistical physics, public health, medicine, epidemiology, applied science, sociology, and agriculture. In many physical situations, it has been observed that many times in the real world, the original variables may be continuous in nature, but discrete by observation. In this study, the α {\rm{\alpha }} -quantile residual life function for discrete lifetime models is defined and some attributes are investigated. The relation between this measure and the hazard rate function is studied. We discuss how this measure could be useful for finding the burn-in time of a lifetime dataset. Then, a new stochastic order based on the α {\rm{\alpha }} -quantile residual life is proposed and studied.

Transmuted cosine Topp-Leone G family of distributions: properties and applications

In contemporary data analysis, the need for flexible and adaptable probabilistic models capable of capturing complex dependencies and tail behaviors in real-life datasets has become increasingly apparent. In light of this demand, A new trigonometric generalized family of distribution, the "Transmuted Cosine Topp-Leone G Family" is proposed in this study. Established on the foundations of, this family combines the adaptability of the Topp-Leone distribution with the periodicity of the cosine function and transmutation theory to produce a flexible framework that may be used to represent a wide range of real-life phenomena. We derive some of the statistical properties of the introduced family such as; survival and hazard functions, and moment and moment-generating functions. Moreover, the model parameters are estimated using the Maximum Likelihood method, and a Monte Carlo simulation was performed to ascertain the behavior and the consistency of the estimates. We investigate the shape of the distribution parameters which results in distributions with left-skew, right-skew, increasing, and decreasing shapes. Lastly, through empirical demonstrations, we showcase the efficacy of the family TrCTLG models in fitting lifetime datasets.

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.

On weighted Amarendra distribution with properties and applications

In this paper some statistical properties including nature of hazard function, mean residual life function, and moments based descriptive statistical constants including coefficient of variation, skweness, kurtosis and index of dispersion of the weighted Amarendra distribution has been discussed. Two methods of estimation, namely, maximum likelihood estimation and maximum product spacing estimation have been discussed. The simulation study has been presented to know the consistency of the estimator of parameters given by the two methods of estimation. Confidence intervals of the parameters are given. The goodness of fit of the distribution has been demonstrated with two real lifetime datasets and the goodness of fit shows that weighted Amarendra distribution provides better fit over weighted Pratibha distribution, weighted Komal distribution, weighted Lindley distribution, weighted Garima distribution, weighted Sujatha distribution, weighted Akash distribution and Gamma distribution.

Adaptive Low-Rank Tensor Estimation Model Based Multichannel Weak Fault Detection for Bearings.

Multichannel signals contain an abundance of fault characteristic information on equipment and show greater potential for weak fault characteristics extraction and early fault detection. However, how to effectively utilize the advantages of multichannel signals with their information richness while eliminating interference components caused by strong background noise and information redundancy to achieve accurate extraction of fault characteristics is still challenging for mechanical fault diagnosis based on multichannel signals. To address this issue, an effective weak fault detection framework for multichannel signals is proposed in this paper. Firstly, the advantages of a tensor on characterizing fault information were displayed, and the low-rank property of multichannel fault signals in a tensor domain is revealed through tensor singular value decomposition. Secondly, to tackle weak fault characteristics extraction from multichannel signals under strong background noise, an adaptive threshold function is introduced, and an adaptive low-rank tensor estimation model is constructed. Thirdly, to further improve the accurate estimation of weak fault characteristics from multichannel signals, a new sparsity metric-oriented parameter optimization strategy is provided for the adaptive low-rank tensor estimation model. Finally, an effective multichannel weak fault detection framework is formed for rolling bearings. Multichannel data from the repeatable simulation, the publicly available XJTU-SY whole lifetime datasets and an accelerated fatigue test of rolling bearings are used to validate the effectiveness and practicality of the proposed method. Excellent results are obtained in multichannel weak fault detection with strong background noise, especially for early fault detection.

Advances in medical data modeling: A new logarithmic beta generated family of distributions with theory and inference

This paper introduces a novel logarithmic beta generated family of distributions, designed specifically for the nuanced analysis of medical data. Through meticulous development, we have establish a comprehensive suite of distributional properties, including quantiles, moments, and hazard rate functions. Central to our contributions is the exploration of the power function distribution, a pivotal sub-model within this innovative family, demonstrating unparalleled flexibility across a broad spectrum of data types. Our investigation delves into seven prominent parameter estimation techniques, rigorously assessing their efficacy through both simulation studies and real-life medical datasets. This comparative analysis highlights the superior performance of the proposed model against existing standards, particularly through improved goodness-of-fit measures across four distinct medical science lifetime datasets. The findings highlight the new model's dominance in capturing complex data patterns, attributable to its adaptable density and hazard rate functions. These attributes significantly enhance modeling capabilities, paving the way for more precise and reliable medical research outcomes. The study concludes by emphasizing the model's potential in advancing statistical methodologies for medical science, backed by theoretical and empirical validations of its superior performance and versatility.

Inference for Compound Exponential XLindley Model with Applications to Lifetime Data

The creating of novel models essentially stems from the requirement to appropriate describe survival cases. In this study, a novel lifetime model with two parameters is proposed and studied for modeling more types of data used in different study cases, including symmetric, asymmetric, skewed, and complex datasets. The proposed model is obtained by compounding the exponential and XLindley distributions, and it is regarded as a strong competitor for the widely applied symmetrical and non-symmetrical models. Several characteristics and statistical properties are investigated. The unknown parameters of the recommended model for the complete sample are estimated using two estimation methods; notably, maximum likelihood estimation and Bayes techniques based on several loss functions as well as an approximate tool are used to construct the confidence intervals for the unknown parameters of the suggested model. The estimation procedures are compared using a Monte Carlo simulation experiment to demonstrate their effectiveness. In the end, the applicability and flexibility of the recommended model are conducted using two real lifetime datasets. In our illustration, we compare the practicality of the recommended model with several well-known competing distributions.

Evaluation of survival weighted Pareto distribution: Analytical properties and applications to industrial and aeronautics data

In statistical modeling, lifetime datasets play an important and significant role. Weighted distributions can be useful to attain the essential purposes relating to the developed distributions’ flexibility and to improve further compliances in data forming; they provide the extension of distributions. The current study suggests a new best-fit probability distribution model based on Pareto distribution. The new model is called Survival Weighted Pareto (SWP) distribution model. Furthermore, the statistical expressions for different properties, which include moments, inverse moments, quantile function, and order statistics, are reported. Moreover, to check the performance and the behavior of different estimators using different sample sizes, a simulation study, which is based on SWP distribution, is performed. According to the simulation results, it is established that the proposed model is a most useful fitted probability model. In addition, an application of the SWP model for three datasets is provided to check the goodness of fit measures of the model.

Development of New Generalized Odd Fréchet-Exponentiated-G Family of Distribution

The study examines the limitations of existing parametric distributional models in accommodating various real-world datasets and proposes an extension termed the New Generalized Odd Fréchet-Exponentiated-G (NGOF-Et-G) family. Building upon prior work, this new distribution model aims to enhance flexibility across datasets by employing the direct substitution method. Mathematical properties including moments, entropy, moment generating function (mgf), and order statistics of the NGOF-Et-G family are analyzed, while parameters are estimated using the maximum likelihood technique. Furthermore, the study introduces the NGOF-Et-Rayleigh and NGOF-Et-Weibull models, evaluating their performance using lifetime datasets. A Monte Carlo simulation is employed to assess the consistency and accuracy of parameter estimation methods, comparing maximum likelihood estimation (MLE) and maximum product spacing (MPS). Results indicate the superiority of MLE in estimating parameters for the introduced distribution, alongside the enhanced flexibility of the new models in fitting positive data compared to existing distributions. In conclusion, the research establishes the potential of the proposed NGOF-Et-G family and its variants as promising alternatives in modelling positive data, offering greater flexibility and improved parameter estimation accuracy, as evidenced by Monte Carlo simulations and real-world dataset applications.

New Odd Generalized Exponentiated Exponential-G Family of Distributions

In the last decades, many researchers have developed new methods for generating families of distributions. These generators are obtained by adding one or more extra shape parameter(s) to the baseline distribution to achieve more flexibility for modelling real lifetime data sets. The additional parameter(s) has been proven useful by obtaining tail properties and improving the analysis from the goodness-of-fit for the families of distributions under study. In this paper, we proposed a new family of distributions called the New Odd Generalized Exponentiated Exponential-G Family of Distributions. The statistical properties are derived, and the maximum likelihood estimation technique is described for the proposed new family of distributions. The new models' performance is illustrated by numerical analysis using a real-life dataset, and the dataset shows that the new models offer a better fit compared to other competing models.

NEW GENERALIZED ODD FRÉCHET-ODD EXPONENTIAL-G FAMILY OF DISTRIBUTION WITH STATISTICAL PROPERTIES AND APPLICATIONS

A new lifetime continuous probability distribution called the new Generalized Odd Fréchet-Odd-Exponential-G Family of Distribution is developed using the principle of Alzaatreh. The developed distribution is flexible for studying positive real-life datasets. The statistical properties related to this family are obtained. The parameters of the family were estimated by using a technique of maximum likelihood. A NewGeneralized Odd Fréchet-Odd-Exponential-Weibull model is introduced. This distribution was fitted with a set of lifetime data. A Monte Carlo simulation is applied to test the consistency of the estimated parameters of this distribution in terms of their bias and mean squared error with a comparison of M.L.E and the maximum product spacing (MPS).The outcome of the Monte Carlo simulation shows that the M.L.E method is the best technique for estimating the parameter of the New Generalized Odd Frechet-Odd-Exponential-Weibull distribution and the New Generalized Odd Frechet-Odd-Exponential-Rayleigh distribution than the M.PS method. The outcomes of the application on the data set produce a higher flexibility than some of the competing distributions. The distributions serve as a viable alternative to other distributions available in the literature for modelling positive data.

Attention features selection oversampling technique (AFS-O) for rolling bearing fault diagnosis with class imbalance

When using data-driven methods for fault diagnosis of mechanical rotating components such as gears and bearings, there is a problem of class imbalance in the lifecycle data collected by sensors. The most commonly used method to address this issue is the synthetic minority over-sampling technique, which synthesizes samples in the feature space, but its blind synthesis may lead to redundant features in the synthetic samples. To avoid this deficiency, this paper proposes a feature-weighted oversampling method called AFS-O (Attention Features Selection Oversampling Technique). First, time–frequency domain features are extracted from the full lifecycle data of bearings to construct an initial subset of features, which serves the input to AFS. Then, AFS is then used to obtain the distribution of feature selection patterns and generate feature weights to determine the inclusion or exclusion of each feature, thereby constructing an optimal subset of features. Finally, the optimal feature subset is synthetically oversampled to achieve class-balanced data, which is then fed into a classifier. AFS-O is applied to the rolling bearing accelerated lifetime dataset from Xi’an Jiaotong University. Experimental results demonstrate that AFS-O outperforms other state-of-the-art synthetic oversampling algorithms in terms of Gmean, , and Recall, confirming the effectiveness of the proposed method.

Exponentially Generated Modified Chen Distribution with Applications to Lifetime Dataset

In this paper, the exponentially generated system was used to modify a two-parameter Chen distribution to a four-parameter distribution with better performance. The property of complete probability distribution function was used to verify the completeness of the resulting distribution, which shows that the distribution is a proper probability distribution function. A simulation study involving varying sample sizes was used to ascertain the asymptotic property of the new distribution. Small and large sample sizes were considered which shows the closeness of the estimates to the true value as the sample size increases. Lifetime dataset were used for model comparison which shows the superiority of exponentially generated modify Chen distribution over some existing distributions. It is therefore recommended to use the four-parameter Chen distribution in place of the well-known two-parameter Chen distribution.

The odd log-logistic generalized exponential distribution: Application on survival times of chemotherapy patients data.

The creation of developing new generalized classes of distributions has attracted applied and theoretical statisticians owing to their properties of flexibility. The development of generalized distribution aims to find distribution flexibility and suitability for available data. In this decade, most authors have developed classes of distributions that are new, to become valuable for applied researchers. This study aims to develop the odd log-logistic generalized exponential distribution (OLLGED), one of the lifetime newly generated distributions in the field of statistics. The advantage of the newly generated distribution is the heavily tailed distributed lifetime data set. Most of the probabilistic properties are derived including generating functions, moments, and quantile and order statistics. Estimation of the model parameter is done by the maximum likelihood method. The performance of parametric estimation is studied through simulation. Application of OLLGED and its flexibilities is done using two data sets and while its performance is done on the randomly simulated data set. The application and flexibility of the OLLGED are ensured through empirical observation using two sets of lifetime data, establishing that the proposed OLLGED can provide a better fit in comparison to existing rival models, such as odd generalized log-logistic, type-II generalized log-logistic, exponential distributions, odd exponential log-logistic, generalized exponential, and log-logistic.

New Generalized Nadarajah Haghighi Distribution: Characterization and Applications

A new Generalized Nadarajah Haghighi (NGNH) distribution following the Exponential T-X (ETX) family was studied. Structural statistical properties and parameter estimation discussed. Simulation study was executed with impressive results. The applicability and usefulness of NGNH was demonstrated using lifetime data sets. The NGNH distribution was compared with other competing distributions.

The Type II Topp-Leone Inverse Power Lomax distribution with Simulation and Applications

In this work, we present a four-parameter lifetime model that can be used to model reliability issues, fatigue life studies, and survival data called the Type II Topp-Leone Inverse Power Lomax distribution. It has the Type II inverse Lomax, Inverse Power Lomax, and Inverse Lomax distributions as sub-models. Some of its statistical properties, including complete and incomplete moments, generating functions, characteristics functions, mean residual life, mean inactivity time, Renyi entropy, Tsallis entropy, order statistics, stress-strength reliability, and weighted probability moment, have formal formulas that we have developed. The model's parameters are estimated using the maximum likelihood estimation technique. The effectiveness of maximum likelihood estimators is evaluated in terms of absolute bias and simulation study standard error. Two lifetime data sets are used to demonstrate how the new model can be applied. Using the same comparative criteria, the proposed distribution offers a better fit than a few well-known distributions.

Parameter Estimation of Inverted Exponentiated Half-Logistic Distribution under Progressive Type-II Censored Data with Competing Risks

In this work, the statistical inference of inverted exponentiated half-logistic distribution is considered under the progressive type-II censored data with competing risks. The parameter estimations of the constant scale parameters but different shape parameters that changed due to various risk factors are investigated in this study. The maximum likelihood estimation is deduced to obtain the parameter estimators and asymptotic confidence intervals; meanwhile, the existence and uniqueness of the maximum likelihood estimators are discussed. Subsequently, bootstrap confidence intervals are calculated and presented. The Bayes estimates based on the square error loss function are derived using the Markov Chain Monte Carlo method. Then, the highest posterior density credible intervals are calculated and provided. Simulations are implemented to compare two kinds of estimates. For illustrative purposes, two experimental lifetime datasets from different fields are exhibited and analyzed. Finally, an optimal censoring scheme is suggested under two optimality criteria.

Transmuted Modified Weibull Distribution for Modeling Skewed Lifetime Dataset; Properties and Application

A new five parameter model called Generalized Modified Weibull distribution is proposed and studied. The new distribution generalizes the Modified Weibull Distribution introduced by Lai et al. (2003) using transformed – Transformer framework of Alzaatreh et al. (2014) which resulted to a distribution capable of modeling skewed data (positively or negatively skewed data), as well as, symmetric data. Property of a proper probability density function was used to ascertain that the resulting function is a proper probability density function. Statistical properties of the newly generated distribution were studied. Graph of probability density function of the distribution was used to show that it is capable of modeling skewed data. Graph of cumulative density functions of the distribution was plotted using varying parameter values. Monte Carlo simulation approach was used for the test of homogeneity of the distribution and it was observed that the parameters in the distribution approach the true values as sample size increases. Maximum likelihood Estimation method was used for estimation of the model parameters. Real life dataset was used for model comparison as well as demonstration of its application.