Lifetime Distribution Research Articles

Bivariate Generalized Exponential Distribution with Positive Probability at (X = 0, Y = 0) and Estimation of Parameters for a Particular Case

Kundu and Gupta, 2009, J Multivar Anal, 100, 581–593, provided a bivariate generalized exponential distribution (BVGED [Formula: see text]), which is a bivariate continuous lifetime distribution. In practice, however, sometimes both the components may fail instantaneously. Thus, we get a mixture bivariate distribution with positive probability at instantaneous failure of each component. The main aim of this article is to define a BVGED with positive probability at instantaneous failure of each component (BVGEDP [Formula: see text]), where PX=0P(X = 0) and P(Y = 0) is a function of parameter [Formula: see text]. It is observed that the joint probability density function and the cumulative distribution function can be expressed in compact forms. Several properties of the distribution have been discussed. For a particular case (BVGEDP ([Formula: see text] 1, 1, 1)), moment type estimators are obtained which are in closed form and maximum likelihood estimators of parameters ([Formula: see text]) are obtained using an iterative procedure. Also, their finite sample and asymptotic properties are discussed using simulation. A final section presents an application to a real data set on which the proposed BVGEDP ([Formula: see text], 1, 1, 1) distribution is fitted. AMS Subject Classification: 62E99

Reliability Analysis for Unknown Age Class of Lifetime Distribution with Real Applications in Medical Science

Analyzing the reliability of the aging class of life distribution provides important information about how long a product lasts and sustainability measures that are essential for determining the environmental impact and formulating resource-saving plans. The study emphasizes the goodness-of-fit technique of the nonparametric test for the NBRUmgf class because age data are crucial for applications. Evaluations were conducted using the test’s asymptotic properties and Pitman efficiency methodology for some selected asymmetric probability models, and the outcomes were compared with those of alternative methods. We assessed the test’s power against widely used reliability distributions for some well-known alternative asymmetric distributions, including the Weibull, Gamma, and linear failure rate (LFR) distributions, and provided percentiles for both censored and uncensored data. This study shows the efficacy of the test in various sectors using real-world datasets and comprehensive tables of test statistics.

Lifetime mapping using femtosecond time-resolved photoemission electron microscopy.

Time-resolved photoemission electron microscopy (PEEM) has established itself as a versatile experimental technique to unravel the ultrafast electron dynamics of materials with nanometer-scale resolution. However, the approach of performing PEEM-based, pixel-by-pixel lifetime mapping has not been reported thus far. Herein, we describe in detail the data pre-processing procedure and an algorithm to perform time-trace fittings of each pixel. We impose an energy cutoff for each pixel prior to spectral integration to enhance the robustness of our approach. With the energy cutoff, the energy-integrated time traces show improved statistics and lower fitting errors, thus resulting in a more accurate determination of the fit parameters, e.g., decay time constants. Our work allows us to reliably construct PEEM-based lifetime maps, which potentially shed light on the effects of local microenvironment on the ultrafast processes of the material and allow spatial distributions of lifetimes to be correlated with observables obtained from complementary microscopic techniques, hence enabling a more comprehensive characterization of the material.

A fuzzy lifetime distribution based assessment of the system’s reliability with a focus on the triskaidecagonal fuzzy number

A fuzzy lifetime distribution based assessment of the system’s reliability with a focus on the triskaidecagonal fuzzy number

Characteristics of the GLLE Family of Lifetime Distributions, and Applications

ABSTRACT. A Generalized Log-Logistic (GLL) family of lifetime distributions is one in which any pair of distributions are related through a GLL transformation, for some (non-negative) value of the transformation parameter (the odds function of the second distribution is the power of the odds function of the first distribution). We consider GLL families generated from an exponential distribution. We derive some useful characteristics of these distributions; moreover, we discuss the hazard rates and Kullback-Leibler divergence, then illustrate the usefulness of this distribution family by fitting real data sets.

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.

Efficient Energy Transfer Enabled by Dark States in van der Waals Heterostructures.

Dark exciton states show great potential in condensed matter physics and optoelectronics because of their long lifetime and rich distribution in band structures. Therefore, they can theoretically serve as efficient energy reservoirs, providing a platform for future applications. However, their optical-transition-forbidden nature severely limits their experimental exploration and hinders their current application. Here, we demonstrate a universal dark state nonlinear energy transfer (ET) mechanism in monolayer WS2/CsPbBr3 van der Waals heterostructures under two-photon excitation, which successfully utilizes the enormous energy reserved in the dark exciton state of CsPbBr3 to significantly improve the photoelectric performance of monolayer WS2. We first propose the scenario of resonant ET between the dark state of CsPbBr3 and WS2, and then reveal that this is a typical Förster resonant ET and belongs to the 2D-2D category. Interestingly, the dark state ET in CsPbBr3 is identified as a long-range donor-bridge-acceptor hopping mode, with a potential distance exceeding 200 nm. Finally, we successfully achieve nearly an order of magnitude enhancement in the near-infrared detection performance of monolayer WS2. Our results enrich the theory of dark exciton states and ET, and they provide a way of using dark exciton states for future practical applications.

Self‐assembled small molecule spherulites under mild conditions: High solid‐state quantum yield and unique interconnected structural and fluorescent colors

AbstractSpherulites are generally fabricated from cooling polymer melts, while their fabrication under mild conditions or from small molecule materials has been barely reported. Besides, organic luminescent molecules typically suffer from low quantum yields in a solid state. Moreover, preparing material with interconnected and simultaneous changes in structural and fluorescent colors is challenging. Here, we present the first solution‐derived spherulites with unique interconnected structural and fluorescent colors, self‐assembled from stearoylated monosaccharides at room temperature. D‐galactose stearoyl ester self‐assembled into banded spherulites, containing twisted nanoplates and interconnected simultaneously changing structural and fluorescent colors. In comparison, D‐mannose stearoyl ester can only form non‐banded spherulites, which contain oriented nanoplates and uniform structural and fluorescent colors. Such materials revealed a novel negative correlation between fluorescence and birefringence, termed alignment‐promoted quenching propensity. Remarkably, the solid‐state fluorescence quantum yields of galactose and mannose‐derived spherulites are as high as 49 ± 2% and 51 ± 2% respectively, approximately ten times higher than those of unmodified monosaccharides. These quantum yield values are among the highest of reported organic nonconventional fluorophores and even comparable to those of conventional aromatic chromophores. Moreover, these spherulites manifested an unexpected excitation‐dependent multicolor photoluminescence with a broad‐spectrum emission (410−620 nm). They show multiple peaks in the photoluminescent emission spectra and broad fluorescence lifetime distributions, which should be attributed to the clustering of a variety of oxygen‐containing functional groups as emissive moieties.

Order-restricted statistical inference and optimal censoring scheme for Gompertz distribution based on joint type-II progressive censored data

This paper considers the order-restricted statistical inference for two populations based on the joint type-II progressive censoring scheme. The lifetime distributions of the two populations are supposed to follow the Gompertz distribution with the same shape parameter but different scale parameters. The maximum likelihood estimates of the unknown parameters are derived by employing the Newton-Raphson algorithm and the expectation-maximization algorithm, respectively. The Fisher information matrix is then employed to construct asymptotic confidence intervals. For Bayes estimation, we assume an ordered Beta-Gamma prior for the scale parameters and a Gamma prior for the common shape parameter. Bayes estimations and the highest posterior density credible intervals for unknown parameters under two different loss functions are obtained with the importance sampling technique. To evaluate the performance of order-restricted inference, extensive Monte Carlo simulations are performed and two air-conditioning systems datasets are used to illustrate the proposed inference methods. In addition, the results are compared with the case when there is no order restriction on the parameters. Finally, the optimal censoring scheme is obtained by four optimality criteria.

Phase-Sensitive Fluorescence Image Correlation Spectroscopy.

Fluorescence lifetime imaging microscopy is sensitive to molecular interactions and environments. In homo-dyne frequency-domain fluorescence lifetime imaging microscopy, images of fluorescence objects are acquired at different phase settings of the detector. The detected intensity as a function of detector phase is a sinusoidal function that is sensitive to the lifetime of the fluorescent species. In this paper, the theory of phase-sensitive fluorescence image correlation spectroscopy is described. In this version of lifetime imaging, image correlation spectroscopy analysis (i.e., spatial autocorrelation) is applied to successive fluorescence images acquired at different phase settings of the detector. Simulations of different types of lifetime distributions reveal that the phase-dependent density of fluorescent objects is dependent on the heterogeneity of lifetimes present in the objects. We provide an example of this analysis workflow to a cervical cancer cell stained with a fluorescent membrane probe.

Stochastic attrition modeling

Lanchester’s equations provide a classical way in which to analyze the performance of two combat teams in battle, competing in the case where they are both equipped comparably and where each team’s survivability is a function of the size of the opposing force. This paper introduces a similar approach motivated by analysis of individual’s statistical lifetime distributions. Applying the same principle as in the design of Lanchester’s equations, a stochastic model is suggested, based upon individual’s lifetimes conditional on the size of the opposing force. This novel approach allows variation in individual team members to be included in the analysis, including the case where team members have correlated lifetimes. Hence, it provides a modeling methodology more general than that available through Lanchester’s equations. Based upon fits to real data, a specific model is then applied for individual lifetimes and it is shown how order statistics of the resultant lifetime distributions may be used to analyze combat team survivability.

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.

Modulating lifetime distribution through variable excitation pulse length and power: a case study on colloidal PbS quantum dots

Modulating lifetime distribution through variable excitation pulse length and power: a case study on colloidal PbS quantum dots

An Analysis of Type-I Generalized Progressive Hybrid Censoring for the One Parameter Logistic-Geometry Lifetime Distribution with Applications

Based on Type-I generalized progressive hybrid censored samples (GPHCSs), the parameter estimate for the unit-half logistic-geometry (UHLG) distribution is investigated in this work. Using maximum likelihood estimation (MLE) and Bayesian estimation, the parameters, reliability, and hazard functions of the UHLG distribution under GPHCSs have been assessed. Likewise, the computation is carried out for the asymptotic confidence intervals (ACIs). Furthermore, two bootstrap CIs, bootstrap-p and bootstrap-t, are mentioned. For symmetric loss functions, like squared error loss (SEL), and asymmetric loss functions, such as linear exponential loss (LL) and general entropy loss (GEL), there are specific Bayesian approximations. The Metropolis–Hastings samplers methodology were used to construct the credible intervals (CRIs). In conclusion, a genuine data set measuring the mortality statistics of a group of male mice with reticulum cell sarcoma is regarded as an application of the methods given.

A Novel Distribution in the Family of Lifetime Distributions for Enhancing Predictive Modeling for Medical and Engineering Data

In nearly all scientific disciplines, the statistical inference about the population rely on handling the sampled data. In the time to event analysis, there are many lifetime distributions to model variation of the lifetime observations based on the shape of hazard rate of the data. In the literature, it has been observed that for non-monotonic hazard the existing distributions do not provide good fits. Practically it is not possible for a distribution to fit any kind of data. Therefore, in this study, a new lifetime distribution is suggested called Flexible Exponentiated Weibull distribution (FEW) to model monotonic and non-monotonic hazard rate data. Maximum likelihood estimation approach is used to estimate the model parameters. In addition to these some prominent statistical properties like, reliability function, moments, hazard function, order statistics, quantile function and entropy measure are obtained. Two real data sets were taken to compare the proposed distribution with existing distributions, and the results showed that the proposed distribution is more flexible than other existing lifetime distributions. Furthermore, simulation study is carried out to check the consistency of model parameters that showed that the parameters are consistent when the sample size increases. These results establish a foundational rationale for selecting the suggested distribution as a model for such a data type. It shows that this distribution is more flexible and suitable for the data studied, making a strong case for choosing it over other options. These findings not only boost trust in the chosen model but also help in deciding how to model similar data in the future.

Reliability estimation and statistical inference under joint progressively Type-II right-censored sampling for certain lifetime distributions

In this article, the parameter estimation of several commonly used two-parameter lifetime distributions, including the Weibull, inverse Gaussian, and Birnbaum–Saunders distributions, based on joint progressively Type-II right-censored sample is studied. Different numerical methods and algorithms are used to compute the maximum likelihood estimates of the unknown model parameters. These methods include the Newton–Raphson method, the stochastic expectation–maximization (SEM) algorithm, and the dual annealing (DA) algorithm. These estimation methods are compared in terms of accuracy (e.g. the bias and mean squared error), computational time and effort (e.g. the required number of iterations), the ability to obtain the largest value of the likelihood, and convergence issues by means of a Monte Carlo simulation study. Recommendations are made based on the simulated results. A real data set is analyzed for illustrative purposes. These methods are implemented in Python, and the computer programs are available from the authors upon request.

Analysis of dependent complementary competing risks data from a generalized inverted family of lifetime distributions under a maximum ranked set sampling procedure with unequal samples

This paper explores analysis of a dependent complementary competing risks model when the failure causes are distributed by the proposed generalized inverted family of lifetime distributions. Under maximum ranked set sampling with unequal samples (MRSSU), statistical inference of model parameters and reliability indices is discussed under classical frequentist and Bayesian approaches, respectively. Maximum likelihood estimators along with their existence and uniqueness are obtained for model parameters, and associated approximate confidence intervals are constructed in consequence. Bayesian estimation is also performed with respect to general flexible priors, and the Markov Chain Monte Carlo (MCMC) algorithm is proposed for complex posterior computation. The study further examines classical and Bayesian estimations with order restriction of parameters when additional historical information is available in the MRSSU scenario. Finally, the performance of different results is evaluated through numerical simulations and a real data example is presented for demonstrating the application of our methods.

Design and Preparation of Lifetime-Based Dual Fluorescent/Phosphorescent Sensor of pH and Oxygen and its Exploration in Model Physiological Solutions and Cells.

In the present report, a novel dual pH-O2 sensor based on covalent conjugate of rhodamine 6G and cyclometalated iridium complex with poly(vinylpyrrolidone-block-vinyltetrazole) copolymer is reported. In model physiological solutions the sensor chromophores display independent phosphorescent and fluorescent lifetime responses onto variations in oxygen concentration and pH, respectively. Colocalization studies on Chinese hamster ovary cells demonstrate the preferential localization in endosomes and lysosomes. The fluorescent lifetime imaging microscopy-phosphorescent lifetime imaging microscopy (FLIM-PLIM) experiments show that the phosphorescent O2 sensor provides unambiguous information onto hypoxia versus normoxia cell status as well as semi-quantitative data on the oxygen concentration in cells in between these two states. However, the results of FLIM measurements indicate that dynamic lifetime interval of the sensor (≈0.5ns between pH values 5.0 and 8.0) is insufficient even for qualitative estimation of pH in living cells because half-width of lifetime distribution in the studied samples is higher than the sensor dynamic interval. Nevertheless, the variations in rhodamine emission intensity are much higher and allow rough discrimination of acidic and neutral cell conditions. Thus, the results of this study indicate that the suggested approach to the design of dual pH-O2 sensors makes possible to prepare the biocompatible and water-soluble conjugate with fast cellular uptake.

A system reliability demonstration test design method based on subsystem test data

AbstractReliability demonstration test (RDT) is the test to verify that the reliability of the product meets the reliability requirements during product development and is usually required to be performed to determine whether it can be accepted. It is essential for complex systems with higher costs. However, the traditional test plans such as the plan in the current RDT standard GJB‐899A have the problem of too long test time or too high risk. In addition, the test data of the complex system itself is usually less, but the test data of the subsystem is easier to obtain. In this paper, the research object is the system, and the main research content is how to use the reliability growth data in the development stage of the subsystem to design the system RDT. First, based on the reliability growth model, the test data in the development stage of the subsystems are modeled to obtain the reliability of each subsystem. The Bayesian theory is used to obtain the lifetime distribution of the system. Then, according to the definition of the two types of risks in the RDT, the life distribution of the product is integrated into the two types of risks, and the RDT plans of the system are designed. Finally, a simulation case is used to verify our RDT design method, and the results show that compared with the traditional plan, our RDT plan designed has a shorter test time and lower test risk.

An inverse lomax-uniform poisson distribution and joint modeling of repeatedly measured and time-to-event data in the health sectors.

Methodological developments in different sectors like health, biomedical and biological areas are the recent burning issue in the statistical literature. The approach of implementing declining hazard function which is obtained by compounding truncated Poisson distribution and a lifetime distribution is a special concern in a few studies. In this paper we proposed a newly introduced distribution called inverse Lomax-Uniform Poisson distribution mostly applied in the health, biomedical, biological, and related sectors. Some basic statistical properties of the distribution are discussed. The capability of the model is checked by comparing it with six potential models by using a practical real data set. Based on the comparison techniques, the newly proposed model out performs all its counterparts. The simulation study is also conducted. Furthermore, the joint modelling of repeatedly measured and time-to-vent processes is discussed in detail with the real data set in the health sector.