Estimation methods for the mean of the exponential distribution based on grouped and censored data

1993 ◽  
Vol 42 (1) ◽  
pp. 87-96 ◽  
Author(s):  
Sun-Keun Seo ◽  
Bong-Jin Yum
Keyword(s):  
Exponential Distribution ◽  
Censored Data ◽  
Estimation Methods ◽  
The Mean

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 Inference for the Exponential Distribution under Generalized Progressively Hybrid Censored Data from Partially Accelerated Life Tests with a Time Transformation Function

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1510
Author(s):  
Alaa H. Abdel-Hamid ◽  
Atef F. Hashem
Keyword(s):  
Exponential Distribution ◽  
Failure Rate ◽  
Censored Data ◽  
Sufficient Conditions ◽  
Transformation Function ◽  
Point Estimation ◽  
Estimation Methods ◽  
Time Transformation ◽  
Monte Carlo Simulation Study ◽  
Accelerated Life

In this article, the tampered failure rate model is used in partially accelerated life testing. A non-decreasing time function, often called a ‘‘time transformation function", is proposed to tamper the failure rate under design conditions. Different types of the proposed function, which have sufficient conditions in order to be accelerating functions, are investigated. A baseline failure rate of the exponential distribution is considered. Some point estimation methods, as well as approximate confidence intervals, for the parameters involved are discussed based on generalized progressively hybrid censored data. The determination of the optimal stress change time is discussed under two different criteria of optimality. A real dataset is employed to explain the theoretical outcomes discussed in this article. Finally, a Monte Carlo simulation study is carried out to examine the performance of the estimation methods and the optimality criteria.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

scholarly journals Potential of spectroscopic analyses for non-destructive estimation of tea quality-related metabolites in fresh new leaves

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hiroto Yamashita ◽  
Rei Sonobe ◽  
Yuhei Hirono ◽  
Akio Morita ◽  
Takashi Ikka
Keyword(s):  
Short Wave ◽  
Machine Learning Algorithms ◽  
Estimation Methods ◽  
Chemical Information ◽  
Tea Quality ◽  
The Mean ◽  
Processing Techniques ◽  
Spectral Patterns ◽  
Physical And Chemical ◽  
Non Destructive

AbstractSpectroscopic sensing provides physical and chemical information in a non-destructive and rapid manner. To develop non-destructive estimation methods of tea quality-related metabolites in fresh leaves, we estimated the contents of free amino acids, catechins, and caffeine in fresh tea leaves using visible to short-wave infrared hyperspectral reflectance data and machine learning algorithms. We acquired these data from approximately 200 new leaves with various status and then constructed the regression model in the combination of six spectral patterns with pre-processing and five algorithms. In most phenotypes, the combination of de-trending pre-processing and Cubist algorithms was robustly selected as the best combination in each round over 100 repetitions that were evaluated based on the ratio of performance to deviation (RPD) values. The mean RPD values were ranged from 1.1 to 2.7 and most of them were above the acceptable or accurate threshold (RPD = 1.4 or 2.0, respectively). Data-based sensitivity analysis identified the important hyperspectral regions around 1500 and 2000 nm. Present spectroscopic approaches indicate that most tea quality-related metabolites can be estimated non-destructively, and pre-processing techniques help to improve its accuracy.

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