scholarly journals Bayesian Estimation Based on Sequential Order Statistics for Heterogeneous Baseline Gompertz Distributions

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 145
Author(s):  
Tzong-Ru Tsai ◽  
Hua Xin ◽  
Chiun-How Kao
Keyword(s):  
Bayesian Estimation ◽  
Hazard Rate ◽  
Estimation Method ◽  
Reliability Evaluation ◽  
Rate Function ◽  
Bayes Estimators ◽  
Multiple Components ◽  
Metropolis Hasting Algorithm ◽  
Evaluation Information

A composite dynamic system (CDS) is composed of multiple components. Each component failure can equally induce higher loading on the surviving components and, hence, enhances the hazard rate of each surviving component. The applications of CDS and the reliability evaluation of CDS has earned more attention in the recent two decades. Because the lifetime quality of components could be inconsistent, the lifetimes of components in the CDS is considered to follow heterogeneous baseline Gompertz distributions in this study. A power-trend hazard rate function is used in order to characterize the hazard rate of the CDS. In order to overcome the difficulty of obtaining reliable estimates of the parameters in the CDS model, the Bayesian estimation method utilizing a hybrid Gibbs sampling and Metropolis-Hasting algorithm to implement the Markov chain Monte Carlo approach is proposed for obtaining the Bayes estimators of the CDS parameters. An intensive simulation study is carried out to evaluate the performance of the proposed estimation method. The simulation results show that the proposed estimation method is reliable in providing reliability evaluation information for the CDS. An example regarding the service system of small electric carts is used for illustration.

scholarly journals Exponentiated Frechet Distribution with Application in Temperature of Assam, India Overview with New Properties and Estimation

2021 ◽  
pp. 211-225
Author(s):  
Umme Habibah Rahman ◽  
Tanusree Deb Roy
Keyword(s):  
Hazard Rate ◽  
Goodness Of Fit ◽  
Survival Function ◽  
Information Matrix ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Rate Function ◽  
Hazard Rate Function ◽  
Fréchet Distribution ◽  
Frechet Distribution

In this paper, a new kind of distribution has suggested with the concept of exponentiate. The reliability analysis including survival function, hazard rate function, reverse hazard rate function and mills ratio has been studied here. Its quantile function and order statistics are also included. Parameters of the distribution are estimated by the method of Maximum Likelihood estimation method along with Fisher information matrix and confidence intervals have also been given. The application has been discussed with the 30 years temperature data of Silchar city, Assam, India. The goodness of fit of the proposed distribution has been compared with Frechet distribution and as a result, for all 12 months, the proposed distribution fits better than the Frechet distribution.

scholarly journals A Two Parameter Odd Exponentiated Skew-T Distribution With J-Shaped Hazard Rate Function

2021 ◽  
Vol 3 (1) ◽  
pp. 26-46
Author(s):  
O. D. Adubisi ◽  
A. Abdulkadir ◽  
H. Chiroma
Keyword(s):  
Hazard Rate ◽  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Rate Function ◽  
Parameter Estimates ◽  
Finite Sample ◽  
T Distribution ◽  
Two Parameter

A new generalization of the skew-t distribution was proposed. The two-parameter lifetime model called the odd exponentiated skew-t distribution has the ability of fitting skewed, long and heavy tailed datasets. It is considered to be more flexible than the skew-t distribution as it contains it as a special case. Some basic properties of the distribution such as the order statistics, entropy, asymptotic behaviour, moment, incomplete moment, characteristic function and quantile function were derived. The odd exponentiated skew-t distribution parameter estimates were derived using the maximum likelihood estimation method and simulation studies performed to evaluate the finite sample performance of these parameter estimates showed that the parameter estimates were consistent and approached the arbitrary selected parameter values as the sample size is increased. The application using a real-life dataset indicated that the new distribution outperformed the other competing distributions. The hazard rate shape of the odd exponentiated skew-t distribution was found to be increasing and J-shaped which was also reflected in the application result.

A NEW CLASS OF TRANSMUTED MODIFIED WEIGHTED WEIBULL DISTRIBUTION AND ITS PROPERTIES

2021 ◽  
Vol 10 (5) ◽  
pp. 2527-2536
Author(s):  
N.I. Badmus ◽  
K.A. Adeleke ◽  
A.A. Olufolabo
Keyword(s):  
Weibull Distribution ◽  
Hazard Rate ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Life Time ◽  
Moment Generating Function ◽  
Rate Function ◽  
Additional Parameter ◽  
Time Data ◽  
Data Set

An additional parameter was added to Modified Weighted Weibull distribution with method of quadratic rank transmutation which led to a newly developed distribution called Transmuted Modified Weighted Weibull distribution. Two distributions that emanated from the new distribution are Transmuted Modified Rayleigh and Transmuted Modified Exponential distributions. Some properties of the distribution that were obtained include; the survival rate, hazard rate, reverse hazard rate function; and moment generating function, mean and variance. Also, parameters of the model were estimated using maximum likelihood estimation method. The model was applied to a life time data set of total milk production of the first birth of 107 cows which showed a better performance compared to some existing known distributions.

scholarly journals A Bimodal Extension of the Exponential Distribution with Applications in Risk Theory

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 679
Author(s):  
Jimmy Reyes ◽  
Emilio Gómez-Déniz ◽  
Héctor W. Gómez ◽  
Enrique Calderín-Ojeda
Keyword(s):  
Exponential Distribution ◽  
Hazard Rate ◽  
Rate Function ◽  
Estimation Methods ◽  
Inverse Gaussian ◽  
New Family ◽  
Tail Distribution ◽  
Zero Values ◽  
The Mean ◽  
Positive Support

There are some generalizations of the classical exponential distribution in the statistical literature that have proven to be helpful in numerous scenarios. Some of these distributions are the families of distributions that were proposed by Marshall and Olkin and Gupta. The disadvantage of these models is the impossibility of fitting data of a bimodal nature of incorporating covariates in the model in a simple way. Some empirical datasets with positive support, such as losses in insurance portfolios, show an excess of zero values and bimodality. For these cases, classical distributions, such as exponential, gamma, Weibull, or inverse Gaussian, to name a few, are unable to explain data of this nature. This paper attempts to fill this gap in the literature by introducing a family of distributions that can be unimodal or bimodal and nests the exponential distribution. Some of its more relevant properties, including moments, kurtosis, Fisher’s asymmetric coefficient, and several estimation methods, are illustrated. Different results that are related to finance and insurance, such as hazard rate function, limited expected value, and the integrated tail distribution, among other measures, are derived. Because of the simplicity of the mean of this distribution, a regression model is also derived. Finally, examples that are based on actuarial data are used to compare this new family with the exponential distribution.

scholarly journals Kumaraswamy Generalized Power Lomax Distributionand Its Applications

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 28-45
Author(s):  
Vasili B.V. Nagarjuna ◽  
R. Vishnu Vardhan ◽  
Christophe Chesneau
Keyword(s):  
Hazard Rate ◽  
Real Data ◽  
Rate Function ◽  
Maximum Likelihood Estimates ◽  
Parameter Estimates ◽  
Parameter Distribution ◽  
Data Sets ◽  
Lomax Distribution ◽  
Entropy Measures ◽  
Modeling Behavior

In this paper, a new five-parameter distribution is proposed using the functionalities of the Kumaraswamy generalized family of distributions and the features of the power Lomax distribution. It is named as Kumaraswamy generalized power Lomax distribution. In a first approach, we derive its main probability and reliability functions, with a visualization of its modeling behavior by considering different parameter combinations. As prime quality, the corresponding hazard rate function is very flexible; it possesses decreasing, increasing and inverted (upside-down) bathtub shapes. Also, decreasing-increasing-decreasing shapes are nicely observed. Some important characteristics of the Kumaraswamy generalized power Lomax distribution are derived, including moments, entropy measures and order statistics. The second approach is statistical. The maximum likelihood estimates of the parameters are described and a brief simulation study shows their effectiveness. Two real data sets are taken to show how the proposed distribution can be applied concretely; parameter estimates are obtained and fitting comparisons are performed with other well-established Lomax based distributions. The Kumaraswamy generalized power Lomax distribution turns out to be best by capturing fine details in the structure of the data considered.

Generalized Birnbaum–Saunders kernel for hazard rate function estimation

2021 ◽  
pp. 1-19
Author(s):  
Sylia Chekkal ◽  
Karima Lagha ◽  
Nabil Zougab
Keyword(s):  
Hazard Rate ◽  
Rate Function ◽  
Hazard Rate Function ◽  
Function Estimation

School Catchment Zone Mergers and Housing Wealth Redistribution

2021 ◽  
pp. 0739456X2110067
Author(s):  
Siu Kei Wong ◽  
Kuang Kuang Deng
Keyword(s):  
School Quality ◽  
Housing Prices ◽  
Estimation Method ◽  
Policy Implications ◽  
Housing Wealth ◽  
Housing Values ◽  
Wealth Redistribution ◽  
The Government ◽  
Empirical Design

This study investigates how perceived school quality affects housing values, using a new estimation method. Our empirical design takes advantage of the mergers of school catchment zones initiated by the government to develop quasi-experiments. We find that, in zones that gained sudden access to higher ranked schools, housing prices increased by 1.3 to 4.1 percent. Larger and more expensive houses appreciated more in response to the improvement in perceived quality of available schools. The findings generate important policy implications regarding housing wealth redistribution and housing expenditures among different households. The study also enriches the literature on the capitalization effect of school quality.

Estimation of Failure Probability and its Applications in Reliability Data Analysis

2010 ◽  
Vol 118-120 ◽  
pp. 601-605
Author(s):  
Han Ming
Keyword(s):  
Parameter Estimation ◽  
Data Analysis ◽  
Bayesian Estimation ◽  
Failure Probability ◽  
Evaluation Method ◽  
Estimation Method ◽  
New Method ◽  
Reliability Parameter ◽  
Hierarchical Bayesian Estimation ◽  
Definition Of

Evaluation method of reliability parameter estimation needs to be improved effectively with the advance of science and technology. This paper develops a new method of parameter estimation, which is named E-Bayesian estimation method. In the case one hyper-parameter, the definition of E-Bayesian estimation of the failure probability is provided, moreover, the formulas of E-Bayesian estimation and hierarchical Bayesian estimation, and the property of E-Bayesian estimation of the failure probability are also provided. Finally, calculation on practical problems shows that the provided method is feasible and easy to perform.

Research on Reliability Evaluation Methods of Distribution System

2014 ◽  
Vol 672-674 ◽  
pp. 1441-1446 ◽  
Author(s):  
Yu Qiang Ou ◽  
Le Feng Cheng ◽  
Jian Zhong Wen ◽  
Xuan Yu Qiu ◽  
Tao Yu
Keyword(s):  
Distribution System ◽  
Evaluation Method ◽  
Network Reliability ◽  
Distribution Network ◽  
Reliability Evaluation ◽  
Evaluation Indexes ◽  
Specific Distribution ◽  
And Function ◽  
Meaning And Function

Research on reliability of distribution network has very important meaning and function to ensure the quality of power supply. This paper introduces some basic concepts of reliability in distribution network, including distribution network reliability definition, task and index. The classical reliability evaluation method was reviewed, and focused on specific distribution network, an example analysis was given, and specific reliability evaluation indexes were calculated. Finally, the future development of distribution network reliability evaluation was made a simple prospect.

Estimation of the Automated Video Control Device’s Target Functions Performance Probability

2021 ◽  
Vol 26 (3-4) ◽  
pp. 291-301
Author(s):  
N.V. Stepanov ◽  
Keyword(s):  
Estimation Method ◽  
Target Function ◽  
Video Camera ◽  
Optimal Receiver ◽  
Efficiency Estimation ◽  
Use Efficiency ◽  
Target Environment ◽  
Receiver Model ◽  
Video Control

Operating quality of automated video control systems depends on optical specifications of video camera and peculiar features of video algorithm. Specified target function performance probability can serve as criterion of automated video control use efficiency. In this work, a new performance efficiency estimation method for automated equipment of target environment video control is suggested: to estimate the probability of target functions’ (object detection, capture, and auto tracking) performance. Theoretical prediction of target functions performance probability was built upon Johnson’s criterion and the use of optimal receiver model. The results of suggested method’s experimental verification have shown that target detection occurred when signal/noise ratio level was above 6. This level can be regarded as low value to ensure that object is detected with probability 0.9.

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