Lifetime Data Sets Research Articles

The Kumaraswamy Unit-Gompertz Distribution and its Application to Lifetime Datasets

This paper presents a new generalized bounded distribution called the Kumaraswamy unit-Gompertz (KUG) distribution. Some of the Mathematical properties which include; the density function, cumulative distribution function, survival and hazard rate functions, quantile, mode, median, moment, moment generating function, Renyi entropy and distribution of order statistics are derived. We employ the maximum likelihood estimation method to estimate the unknown parameters of the proposed KUG distribution. A Monte Carlo simulation study is carried out to investigate the performance of the maximum likelihood estimates of the unknown parameters of the proposed distribution. Two real datasets are used to illustrate the applicability of the proposed KUG distribution in lifetime data analysis.

Discrete Bilal Distribution in the Presence of Right-Censored Data and a Cure Fraction

The statistical literature presents many continuous probability distributions with only one parameter, which are extensively used in the analysis of lifetime data, such as the exponential, the Lindley, and the Rayleigh distributions. Alternatively, the use of discretized versions of these distributions can provide a better fit for the data in many applications. As the novelty of this study, we present inferences for the discrete Bilal distribution (DB) with one parameter introduced by Altun et al. (2020) in the presence of right-censored data and cure fraction. We assume standard maximum likelihood methods based on asymptotic normality of the maximum likelihood estimators and also a Bayesian approach based on MCMC (Markov Chain Monte Carlo) simulation methods to get inferences for the parameters of the discrete BD distribution. The use of the proposed model was illustrated with three examples considering real medical lifetime data sets. From these applications, we concluded that the proposed model based on the discrete DB distribution has good performance even with the inclusion of a cure fraction in comparison to other existing discrete models, such as the DsFx-I, Lindley, Rayleigh, and Burr-Hatke probability distributions. Moreover, the model can be easily implemented in standard existing software, such as the R package. Under a Bayesian approach, we assumed a gamma prior distribution for the parameter of the DB discrete distribution. We also provided a brief sensitivity analysis assuming the half-normal distribution in place of the gamma distribution for the parameter of the DB distribution. From the obtained results of this study, we can conclude that the proposed methodology can be very useful for researchers dealing with medical discrete lifetime data in the presence of right-censored data and cure fraction.

Bivariate Generalized Half-Logistic Distribution: Properties and Its Application in Household Financial Affordability in KSA

The generalized half-logistic distribution is ideal to fit the lifetime of some products, such as ball bearings and electrical insulation. In this paper, we aim to extend this scope by creating a motivated bivariate version. We thus introduce the bivariate generalized half-logistic distribution using the Farlie Gumbel Morgenstern (FGM) copula, which is called the FGM bivariate generalized half-logistic distribution (FGMBGHLD for short). In particular, the FGMBGHLD finds application in describing bivariate lifetime datasets that have weak correlations between variables. Some statistical properties and functions of our new distribution, such as the product moments, moment generating function, reliability function, and hazard rate function, are derived. We discuss the maximum likelihood estimation method of the FGMBGHLD parameters. As an application of the FGMBGHLD in reliability, we consider the stress–strength model when the stress and strength random variables are dependent. We also derive the point and interval estimates of the stress–strength coefficient. Finally, we use the data from the household income and expenditure survey of KSA 2018 for Saudi households by administrative region to demonstrate the practicability of the proposed model. A comparison with a modern bivariate Weibull distribution is performed.

Inference of competing risks Chen lifetime populations under type-I censoring scheme when causes of failure are partially observed

In this paper, we adopted the competing risks model considering that, the failure time is distributed with the Chen lifetime distribution, causes of failure are partially observed and the individuals are tested under type-I censoring scheme. The model parameters are estimated by maximum likelihood and Bayes estimations. Also, the asymptotic confidence intervals as well as credible interval are constructed. The proposed model is used to analyze two sets of data, real and simulate lifetime data sets for illustrative purposes.

Statistical Properties and Applications of Exponentiated Inverse Power Cauchy Distribution

In this article, we have introduced the new distribution named exponentiated inverse power Cauchy distribution, which presents more flexibility in modeling a real lifetime dataset. The proposed distribution is analytically appealing and easy to work with and can be used efficiently to analyze the real data sets. Its probability density function can include various shapes according to the value of the parameters. Different explicit expressions for its quantile, survival, hazard and generating function, density function of the order statistics, cumulative hazard function, and failure rate function are provided. The model’s parameters are estimated by using the maximum likelihood estimation method, and we also obtained the observed information matrix. We have also constructed the asymptotic confidence intervals for the estimated parameters of the proposed distribution. We have illustrated the goodness-of-fit test and the application of the purposed distribution empirically through a real-life data set. All the computations are performed in R software (version 4.1.1). It is observed that the proposed distribution gets at least similar or a better fit than some selected distributions taken for comparison.

Zero Truncated Poisson Harris Weibull Distribution: Properties and Applications to Lifetime Datas

In this study, we proposed and developed a more flexible distribution with wider applications called Zero Truncated Poisson Harris Weibull (ZTPHW) distribution. Some well-known mathematical properties such as ordinary moments and incomplete moment, moment generating function, quantile function, Renyi and Tsallis entropy of ZTPHW distribution are investigated. The expressions of order statistics are derived. Parameters of the derived distribution are obtained using the maximum likelihood method and simulation studied is carried out to examine the validity of the method of estimation. The flexibility of the proposed distribution in modeling real life data is demonstrated using two lifetime data set.

New Reprocessing towards Life-Time Quality-Consistent Suomi NPP OMPS Nadir Sensor Data Records (SDR): Calibration Improvements and Impact Assessments on Long-Term Quality Stability of OMPS SDR Data Sets

The Nadir Mapper (NM) and Nadir Profiler (NP) within the Ozone Mapping and Profiler Suites (OMPS) are ultraviolet spectrometers to measure Earth radiance and Solar irradiance spectra from 300–380 nm and 250–310 nm, respectively. The OMPS NM and NP instruments flying on the Suomi-NPP (SNPP) satellite have provided over ten years of operational Sensor Data Records (SDRs) data sets to support a variety of OMPS Environmental Data Record (EDR) applications. However, the discrepancies of quality remain in the operational OMPS SDR data prior to 28 June 2021 due to changes in calibration algorithms associated with the calibration coefficient look-up tables (LUTs) during this period. In this study, we present results for the newly (v2) reprocessed SNPP OMPS NM and NP SDR data prior to 30 June 2021, which uses consistent calibration tables with improved accuracy. Compared with a previous (v1) reprocessing, this new reprocessing includes the improvements associated with the following updated tables or error correction: an updated stray light correction table for the NM, an off-nadir geolocation error correction for the NM, an artificial offset error correction in the NM dark processing code, and biweekly solar wavelength LUTs for the NP. This study further analyzes the impact of each improvement on the quality of the OMPS SDR data by taking advantage of the existing OMPS SDR calibration/validation studies. Finally, this study compares the v2 reprocessed OMPS data sets with the operational and the v1 reprocessed data sets. The results demonstrate that the new reprocessing significantly improves the accuracy and consistency of the life-time SNPP OMPS NM and NP SDR data sets. It also advances the uniformity of the data over the dichroic range from 300 to 310 nm between the NM and NP. The normalized radiance differences at the same wavelength between the NM and NP observations are reduced from 0.001 order (v1 reprocessing) or 0.01 order (operational processing) to 0.001 order or smaller. The v2 reprocessed data are archived in the NOAA CLASS data center with the same format as the operational data.

A new generalized family of distributions based on combining Marshal-Olkin transformation with T-X family.

Data analysis in real life often relies mainly on statistical probability distributions. However, data arising from different fields such as environmental, financial, biomedical sciences and other areas may not fit the classical distributions. Therefore, the need arises for developing new distributions that would capture high degree of skewness and kurtosis and enhance the goodness-of-fit in empirical distribution. In this paper, we introduce a novel family of distributions which can extend some popular classes of distributions to include different new versions of the baseline distributions. The proposed family of distributions is referred as the Marshall-Olkin Weibull generated family. The proposed family of distributions is a combination of Marshall-Olkin transformation and the Weibull generated family. Two special members of the proposed family are investigated. A variety of shapes for the densities and hazard rate are presented of the considered sub-models. Some of the main mathematical properties of this family are derived. The estimation for the parameters is obtained via the maximum likelihood method. Moreover, the performance of the estimators for the considered members is examined through simulation studies in terms of bias and root mean square error. Besides, based on the new generated family, the log Marshall-Olkin Weibull-Weibull regression model for censored data is proposed. Finally, COVID-19 data and three lifetime data sets are used to demonstrate the importance of the newly proposed family. Through such an applications, it is shown that this family of distributions provides a better fit when compared with other competitive distributions.

Study of the New Finite Mixture of Weibull Extension Model: Identifiability, Properties and Estimation

Finite mixture models have been used in many fields of statistical analysis such as pattern recognition, clustering and survival analysis, and have been extensively applied in different scientific areas such as marketing, economics, medicine, genetics and social sciences. Introducing mixtures of new generalized lifetime distributions that exhibit important hazard shapes is a major field of research aiming at fitting and analyzing a wider variety of data sets. The main objective of this article is to present a full mathematical study of the properties of the new finite mixture of the three-parameter Weibull extension model, considered as a generalization of the standard Weibull distribution. The new proposed mixture model exhibits a bathtub-shaped hazard rate among other important shapes in reliability applications. We analytically prove the identifiability of the new mixture and investigate its mathematical properties and hazard rate function. Maximum likelihood estimation of the model parameters is considered. The Kolmogrov-Smirnov test statistic is used to fit two famous data sets from mechanical engineering to the proposed model, the Aarset data and the Meeker and Escobar datasets. Results show that the two-component version of the proposed mixture is a superior fit compared to various lifetime distributions, either one-component or two-component lifetime distributions. The new proposed mixture is a significant statistical tool to study lifetime data sets in numerous fields of study.

On record based transmuted inverse exponential distribution

Inverse Exponential distribution has been used to analyze lifetime datasets which has non monotone hazard function and has applications in reliability and biological study areas. The present study introduces new generalization of inverse exponential distribution using Record-Based transmutation. Record-Based transmuted inverse Exponential distribution is derived and its properties studied. The maximum likelihood estimation procedure is employed to estimate the parameters of the proposed distribution. Finally, an algorithm in R package is developed to carry out the simulation studies.

Lindley Generalized Inverted Exponential Distribution: Model and Applications

In this article, we have proposed three parameters distribution using lindley family of distribution and Generalized inverted Exponential distribution called Lindley Generalized Inverted Exponential Distribution: Model and Applications(LGIE). The statistical properties as well as different characteristics like the hazard rate function (HRF), the probability density function (PDF), the cumulative distribution function (CDF), quantile function , skewness, and kurtosis of the proposed distribution are discussed. The parameters of the proposed distribution are estimated by using the maximum likelihood estimation (MLE), least-square estimation (LSE) and Cramer-Von-Mises (CVM) methods. All the computations are performed in R programming software. To assess the application of the proposed distribution, a real lifetime data set is analyzed and performed the goodness-of-fit.

Alpha Power Extended Inverse Weibull Poisson Distribution: Properties, Inference, and Applications to lifetime data

In this paper, a new four-parameter extended inverse Weibull distribution called Alpha power Extended Inverse Weibull Poisson distribution is introduced using the alpha power Poisson generator. This method adds two shape parameters to a baseline distribution thereby increasing its flexibility and applicability in modeling lifetime data. We study the structural properties of the new distribution such as the mean, variance, quantile function, median, ordinary and incomplete moments, reliability analysis, Lorenz and Bonferroni curves, Renyi entropy, mean waiting time, mean residual life, and order statistics. We use the method of maximum likelihood technique for estimating the model parameters of Alpha power extended inverse Weibull distribution and the corresponding confidence intervals are obtained. The simulation method is carried out to evaluate the performance of the maximum likelihood estimate in terms of their Absolute Bias and Mean Square Error using simulated data. Two lifetime data sets are presented to demonstrate the applicability of the new model and it is found that the new model has superior modeling power when compare to Inverse Weibull distribution, Alpha Power Poisson inverse exponential distribution, Alpha Power Extended Inverse Weibull distribution, and Alpha Power Extended Inverse Exponential distribution.

A new generalization of logistic Weibull distribution with theory and practical illustration

This study developed the exponentiated logistic Weibull distribution as a new generality of the logistic Weibull distribution to deal with real-life data sets. The newly developed model has numerous sub-models such as the logistic exponential, logistic Rayleigh, and the exponentiated logistic Rayleigh distribution revealed in the literature. We have derived and studied essential properties of the including moments, probability weighted moments, quantile function, entropies and stress-strength reliability. The maximum likelihood estimation method is being used to estimate the parameters efficiently. However, the Monte Carlos simulation study is used to observe the behavior of estimated parameters at different sample values based on bias and mean square error. Moreover, it is justified that the exponentiated logistic Weibull distribution can be used as a better alternative as compared to the other generalization of the Weibull distribution for lifetime data sets. It has observed from two-lifetime data sets that the newly developed model was a better fit as compared to other considered generalizations of the Weibull distribution.

Generalized Inverse Power Sujatha Distribution with Applications

In this paper, we present a new lifetime distribution known as the generalized inverse power Sujatha distribution. The statistical and mathematical properties of the new distribution such as the moment and moment generating function, Renyi entropy and distribution of order statistics have been derived and discussed. Also, reliability measures like survival function, hazard function, reverse hazard rate, cumulative hazard rate and odds function are discussed. Maximum likelihood estimation technique was used to estimate the parameters. However, a 95% confidence intervals were constructed for the parameters. Finally, we applied the proposed distribution to two lifetime datasets and compare its superiority over other candidate models. Results obtained indicates that the generalized inverse power Sujatha distribution outperform the other competing models.

Early Fault Diagnosis Technology for Bearings Based on Quantile Multiscale Permutation Entropy

Early fault diagnosis of bearings is the basis of condition-based maintenance. To overcome the difficulty of early fault diagnosis for the mechanical system, a new conception named quantile multiscale permutation entropy (QMPE) is defined, and a new feature extraction method based on QMPE is proposed. On the basis of the multiscale entropy, the multiscale permutation entropy for the gathered vibration signal of equipment is obtained, and the sample quantile is calculated, which is employed to analyze the weak change of the variation signal. The proposed method is verified with the full lifetime datasets of a certain bearing, which proves that signal features extracted by the QMPE method can not only truly express the bearing detailed condition changing from normal to fault but also duly detect the early fault of the bearing. Comparing with other methods for early fault diagnosis, the proposed method can advance the finding time of the early fault obviously.

Nonparametric sequential estimation of the cumulative function by orthogonal series and application in reliability

This article proposes the orthogonal series method for the cumulative distribution function estimation based on a random number of observations Nt , which may be recorded in time We give the statistical properties of the estimator (bias, variance, mean square error, mean square integrated error, and the rate of convergence) and some asymptotic properties. We consider that Nt is independent of the observations and as The choice of the smoothing parameter (bandwidth) of the estimator is investigated by two methods: The Kronmal–Tarter method and a new technique proposed by Saadi et al. adapted to the random sample size case. A detailed study with a Dirichlet basis is presented. The obtained estimator is asymptotically unbiased and consistent. An application to the reliability field is investigated with simulations in order to study the behavior of the reliability and failure rate estimators, from different life distributions, namely: Lognormal, Gamma, and Weibull distributions. A real lifetime data sets are analyzed by our proposed approach. The results show that the proposed estimators are performant.

Robust Assessing the Lifetime Performance of Products with Inverse Gaussian Distribution in Bayesian and Classical Setup

The inverse Gaussian (Wald) distribution belongs to the two-parameter family of continuous distributions having a range from 0 to ∞ and is considered as a potential candidate to model diffusion processes and lifetime datasets. Bayesian analysis is a modern inferential technique in which we estimate the parameters of the posterior distribution obtained by formally combining a prior distribution with an observed data distribution. In this article, we have attempted to perform the Bayesian and classical analyses of the Wald distribution and compare the results. Jeffreys' and uniform priors are used as noninformative priors, while the exponential distribution is used as an informative prior. The analysis comprises finding joint posterior distributions, the posterior means, predictive distributions, and credible intervals. To illustrate the entire estimation procedure, we have used real and simulated datasets, and the results thus obtained are discussed and compared. We have used the Bayesian specialized Open BUGS software to perform Markov Chain Monte Carlo (MCMC) simulations using a real dataset.

The Topp-Leone Weibull Distribution: Its Properties and Application

This paper presents a new generalization of the Topp-Leone distribution called the Topp-Leone Weibull Distribution (TLWD). Some of the mathematical properties of the proposed distribution are derived, and the maximum likelihood estimation method is adopted in estimating the parameters of the proposed distribution. An application of the proposed distribution alongside with some well-known distributions belonging to the Topp-Leone generated family of distributions, to a real lifetime data set reveals that the proposed distribution exhibits more flexibility in modeling lifetime data based on some comparison criteria such as maximized log-likelihood, Akaike Information Criterion [AIC=2k-2 log⁡(L) ], Kolmogorov-Smirnov test statistic (K-S) and Anderson Darling test statistic (A*) and Crammer-Von Mises test statistic (W*).

The Comparison Between Gumbel and Exponentiated Gumbel Distributions and Their Applications in Hydrological Process

The Exponentiated Gumbel (EG) distribution has been proposed to capture some aspects of the data that the Gumbel distribution fails to specify. it has an increasing hazard rate. The Exponentiated Gumbel distribution has applications in hydrology, meteorology, climatology, insurance, finance and geology, among many others. In this paper Firstly, the mathematical and statistical characteristics of the gumbel and Exponentiated Gumbel distribution are presented, then the applications of this distributions are studied using the real data set. Its first moment about origin and moments about mean have been obtained and expressions for skewness, kurtosis have been given. Estimation of its parameter has been discussed using the method of maximum likelihood. In the end, two applications of the gumbel and exponentiated gumbel distribution have been discussed with two real lifetime data sets. The results also confirmed the suitability of the Exponentiated Gumbel distribution for real data collection.

Lifetime Observation of Cognition and Physiological Parameters in Male Mice.

Laboratory mice are predominantly used for one experiment only, i.e., new mice are ordered or bred for every new experiment. Moreover, most experiments use relatively young mice in the range of late adolescence to early adulthood. As a consequence, little is known about the day-to-day life of adult and aged laboratory mice. Here we present a long-term data set with three consecutive phases conducted with the same male mice over their lifetime in order to shed light on possible long-term effects of repeated cognitive stimulation. One third of the animals was trained by a variety of learning tasks conducted up to an age of 606 days. The mice were housed in four cages with 12 animals per cage; only four mice per cage had to repeatedly solve cognitive tasks for getting access to water using the IntelliCage system. In addition, these learner mice were tested in standard cognitive tests outside their home-cage. The other eight mice served as two control groups living in the same environment but without having to solve tasks for getting access to water. One control group was additionally placed on the test set-ups without having to learn the tasks. Next to the cognitive tasks, we took physiological measures (body mass, resting metabolic rate) and tested for dominance behavior, and attractivity in a female choice experiment. Overall, the mice were under surveillance until they died a natural death, providing a unique data set over the course of virtually their entire lives. Our data showed treatment differences during the first phase of our lifetime data set. Young learner mice showed a higher activity, less growth and resting metabolic rate, and were less attractive for female mice. These effects, however, were not preserved over the long-term. We also did not find differences in dominance or effects on longevity. However, we generated a unique and valuable set of long-term behavioral and physiological data from a single group of male mice and note that our long-term data contribute to a better understanding of the behavioral and physiological processes in male C57Bl/6J mice.