scholarly journals A Distribution for Instantaneous Failures

Stats ◽  
2019 ◽  
Vol 2 (2) ◽  
pp. 247-258 ◽  
Author(s):  
Pedro L. Ramos ◽  
Francisco Louzada
Keyword(s):  
Residual Life ◽  
Likelihood Estimation ◽  
Estimation Methods ◽  
Mean Residual Life ◽  
Parameter Distribution ◽  
Coverage Probabilities ◽  
Instantaneous Failures ◽  
The Relationship ◽  
Mean Variance ◽  
New Distribution

A new one-parameter distribution is proposed in this paper. The new distribution allows for the occurrence of instantaneous failures (inliers) that are natural in many areas. Closed-form expressions are obtained for the moments, mean, variance, a coefficient of variation, skewness, kurtosis, and mean residual life. The relationship between the new distribution with the exponential and Lindley distributions is presented. The new distribution can be viewed as a combination of a reparametrized version of the Zakerzadeh and Dolati distribution with a particular case of the gamma model and the occurrence of zero value. The parameter estimation is discussed under the method of moments and the maximum likelihood estimation. A simulation study is performed to verify the efficiency of both estimation methods by computing the bias, mean squared errors, and coverage probabilities. The superiority of the proposed distribution and some of its concurrent distributions are tested by analyzing four real lifetime datasets.

scholarly journals A New Inverted Topp-Leone Distribution: Applications to the COVID-19 Mortality Rate in Two Different Countries

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 25 ◽  
Author(s):  
Ehab Almetwally ◽  
Randa Alharbi ◽  
Dalia Alnagar ◽  
Eslam Hafez
Keyword(s):  
Statistical Model ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Likelihood Estimation ◽  
Linear Representation ◽  
Rate Function ◽  
Estimation Methods ◽  
Unknown Parameters ◽  
Least Squares Estimators ◽  
New Distribution

This paper aims to find a statistical model for the COVID-19 spread in the United Kingdom and Canada. We used an efficient and superior model for fitting the COVID 19 mortality rates in these countries by specifying an optimal statistical model. A new lifetime distribution with two-parameter is introduced by a combination of inverted Topp-Leone distribution and modified Kies family to produce the modified Kies inverted Topp-Leone (MKITL) distribution, which covers a lot of application that both the traditional inverted Topp-Leone and the modified Kies provide poor fitting for them. This new distribution has many valuable properties as simple linear representation, hazard rate function, and moment function. We made several methods of estimations as maximum likelihood estimation, least squares estimators, weighted least-squares estimators, maximum product spacing, Crame´r-von Mises estimators, and Anderson-Darling estimators methods are applied to estimate the unknown parameters of MKITL distribution. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. also, we applied different data sets to the new distribution to assess its performance in modeling data.

The hazard and vitality measures of ageing

1989 ◽  
Vol 26 (03) ◽  
pp. 532-542 ◽  
Author(s):  
Joseph Kupka ◽  
Sonny Loo
Keyword(s):  
Sudden Death ◽  
Failure Rate ◽  
Residual Life ◽  
Ageing Process ◽  
Mean Residual Life ◽  
Absolutely Continuous ◽  
Intrinsic Interest ◽  
Increasing Failure Rate ◽  
Time Period ◽  
The Relationship

A new measure of the ageing process called the vitality measure is introduced. It measures the ‘vitality' of a time period in terms of the increase in average lifespan which results from surviving that time period. Apart from intrinsic interest, the vitality measure clarifies the relationship between the familiar properties of increasing hazard and decreasing mean residual life. The main theorem asserts that increasing hazard is equivalent to the requirement that mean residual life decreases faster than vitality. It is also shown for general (i.e. not necessarily absolutely continuous) distributions that the properties of increasing hazard, increasing failure rate, and increasing probability of ‘sudden death' are all equivalent.

ROLLER-COASTER FAILURE RATES AND MEAN RESIDUAL LIFE FUNCTIONS WITH APPLICATION TO THE EXTENDED GENERALIZED INVERSE GAUSSIAN MODEL

2010 ◽  
Vol 25 (1) ◽  
pp. 103-118 ◽  
Author(s):  
Ramesh C. Gupta ◽  
Weston Viles
Keyword(s):  
Failure Rate ◽  
Generalized Inverse ◽  
Residual Life ◽  
Gaussian Model ◽  
Change Points ◽  
Mean Residual Life ◽  
Additional Parameter ◽  
Inverse Gaussian ◽  
Generalized Inverse Gaussian ◽  
The Relationship

The investigation in this article was motivated by an extended generalized inverse Gaussian (EGIG) distribution, which has more than one turning point of the failure rate for certain values of the parameters. In order to study the turning points of a failure rate, we appeal to Glaser's eta function, which is much simpler to handle. We present some general results for studying the reationship among the change points of Glaser's eta function, the failure rate, and the mean residual life function (MRLF). Additionally we establish an ordering among the number of change points of Glaser's eta function, the failure rate, and the MRLF. These results are used to investigate, in detail, the monotonicity of the three functions in the case of the EGIG. The EGIG model has one additional parameter, δ, than the generalized inverse Gaussian (GIG) model's three parameters; see Jorgensen [7]. It has been observed that the EGIG model fits certain datasets better than the GIG of Jorgensen [7]. Thus, the purpose of this article is to present some general results dealing with the relationship among the change points of the three functions described earlier. The EGIG model is used as an illustration.

The Estimated Probability of Dizygotic Twins: A Comparison of Two Methods

2009 ◽  
Vol 12 (1) ◽  
pp. 79-85 ◽  
Author(s):  
Jill Hardin ◽  
Steve Selvin ◽  
Suzan L. Carmichael ◽  
Gary M. Shaw
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Data Sources ◽  
Maximum Likelihood Estimates ◽  
Estimation Methods ◽  
Dizygotic Twin ◽  
Twin Data ◽  
Dizygotic Twins ◽  
The Relationship

AbstractThis study presents a general model of two binary variables and applies it to twin sex pairing data from 21 twin data sources to estimate the frequency of dizygotic twins. The purpose of this study is to clarify the relationship between maximum likelihood and Weinberg's differential rule zygosity estimation methods. We explore the accuracy of these zygosity estimation measures in relation to twin ascertainment methods and the probability of a male. Twin sex pairing data from 21 twin data sources representing 15 countries was collected for use in this study. Maximum likelihood estimation of the probability of dizygotic twins is applied to describe the variation in the frequency of dizygotic twin births. The differences between maximum likelihood and Weinberg's differential rule zygosity estimation methods are presented as a function of twin data ascertainment method and the probability of a male. Maximum likelihood estimation of the probability of dizygotic twins ranges from 0.083 (95% approximate CI: 0.082, 0.085) to 0.750 (95% approximate CI: 0.749, 0.752) for voluntary ascertainment data sources and from 0.374 (95% approximate CI: 0.373, 0.375) to 0.987 (95% approximate CI: 0.959, 1.016) for active ascertainment data sources. In 17 of the 21 twin data sources differences of 0.01 or less occur between maximum likelihood and Weinberg zygosity estimation methods. The Weinberg and maximum likelihood estimates are negligibly different in most applications. Using the above general maximum likelihood estimate, the probability of a dizygotic twin is subject to substantial variation that is largely a function of twin data ascertainment method.

RELIABILITY PROPERTIES OF MEAN TIME TO FAILURE IN AGE REPLACEMENT MODELS

2010 ◽  
Vol 17 (01) ◽  
pp. 15-26 ◽  
Author(s):  
G. ASHA ◽  
N. UNNIKRISHNAN NAIR
Keyword(s):  
Residual Life ◽  
Stochastic Orders ◽  
Mean Residual Life ◽  
Time To Failure ◽  
Mean Time To Failure ◽  
Replacement Model ◽  
The Mean ◽  
Age Replacement ◽  
The Relationship ◽  
Mean Time

In this article some properties of the mean time to failure in an age replacement model is presented by examining the relationship it has with hazard (reversed hazard) rate and mean (reversed mean) residual life functions. An ordering based on mean time to failure is used to examine its implications with other stochastic orders.

scholarly journals Fisher consistent estimation of regression parameter in the proportional mean residual life model with frailty

Ekonomia ◽  
2021 ◽  
Vol 27 (2) ◽  
pp. 81-88
Author(s):  
Magdalena Skolimowska-Kulig
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Regression Models ◽  
Residual Life ◽  
Likelihood Estimation ◽  
Mean Residual Life ◽  
Regression Parameter ◽  
Consistent Estimation ◽  
Regression Parameters ◽  
Life Model

In the article, we consider the Fisher consistent estimation of the regression parameters in the proportional mean residual life model with arbitrary frailty. It is discussed that conventional estimation procedures, such as the maximum likelihood estimation or Cox’s approach, which are employed in common regression models, may also yield consistent inference in the extended models.

scholarly journals Statistical Properties & Different Methods Of Estimation Of A New Extended Weighted Frechet Distribution.

2021 ◽  
Vol 12 (6) ◽  
pp. 1011-1029
Author(s):  
Mahdi Wahhab Neamah , Et. al.
Keyword(s):  
Statistical Properties ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Percentile Method ◽  
Fréchet Distribution ◽  
Coefficients Of Variation ◽  
Coefficient Of Skewness ◽  
Frechet Distribution ◽  
Mean Variance ◽  
New Distribution

In this paper, we introduce a new distribution is called the extended weighted Frechet distribution, which we obtain by applying the Azzalini method and deduced some statistical properties such as mean, variance, coefficients of variation, coefficient of skewness, and coefficient of kurtosis. The parameters of the new distribution were estimated by the following estimation methods: Maximum Likelihood Method (MLE) and percentile method. We used the Monte Carlo simulation to compare the performances of the proposed estimators obtained through methods of estimation.

scholarly journals Odoma Distribution and Its Application

2019 ◽  
pp. 1-11
Author(s):  
C. C. Odom ◽  
M. A. Ijomah
Keyword(s):  
Goodness Of Fit ◽  
Residual Life ◽  
Survival Function ◽  
Real Life ◽  
Rate Function ◽  
Mean Residual Life ◽  
Mathematical Properties ◽  
Real Life Data ◽  
Method Of Maximum Likelihood ◽  
New Distribution

In this study, a new continuous one parameter lifetime distribution is proposed. Its mathematical properties such as moments, order statistics, entropy, survival function, hazard rate function and mean residual life function are derived. The new distribution is applied to real-life data from engineering and the method of maximum likelihood is used to estimate the parameter. The goodness-of-fit of the new distribution shows its better fit to the data than some competing distributions.

scholarly journals A GENERALIZATION OF SUJATHA DISTRIBUTION AND ITS APPLICATIONS WITH REAL LIFETIME DATA

2017 ◽  
Vol 22 (1) ◽  
pp. 66-83 ◽  
Author(s):  
Rama Shanker ◽  
Kamlesh Kumar Shukla ◽  
Hagos Fesshaye
Keyword(s):  
Residual Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Stochastic Ordering ◽  
Rate Function ◽  
Mean Residual Life ◽  
Exponential Distributions ◽  
Lorenz Curves ◽  
Two Parameter ◽  
Life Function

A two-parameter generalization of Sujatha distribution (AGSD), which includes Lindley distribution and Sujatha distribution as particular cases, has been proposed. It's important mathematical and statistical properties including its shape for varying values of parameters, moments, coefficient of variation, skewness, kurtosis, index of dispersion, hazard rate function, mean residual life function, stochastic ordering, mean deviations, Bonferroni and Lorenz curves, and stress-strength reliability have been discussed. Maximum likelihood estimation method has been discussed for estimating its parameters. AGSD provides better fit than Sujatha, Aradhana, Lindley and exponential distributions for modeling real lifetime data.Journal of Institute of Science and TechnologyVolume 22, Issue 1, July 2017, Page: 66-83

scholarly journals A Novel Method for Developing Efficient Probability Distributions with Applications to Engineering and Life Science Data

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Alamgir Khalil ◽  
Abdullah Ali H. Ahmadini ◽  
Muhammad Ali ◽  
Wali Khan Mashwani ◽  
Shokrya S. Alshqaq ◽  
...  
Keyword(s):  
Residual Life ◽  
Probability Distributions ◽  
Probability Model ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Strength Parameter ◽  
Mean Residual Life ◽  
Simulation Studies ◽  
Science Data ◽  
Proposed Model

In this paper, a new approach for deriving continuous probability distributions is developed by incorporating an extra parameter to the existing distributions. Frechet distribution is used as a submodel for an illustration to have a new continuous probability model, termed as modified Frechet (MF) distribution. Several important statistical properties such as moments, order statistics, quantile function, stress-strength parameter, mean residual life function, and mode have been derived for the proposed distribution. In order to estimate the parameters of MF distribution, the maximum likelihood estimation (MLE) method is used. To evaluate the performance of the proposed model, two real datasets are considered. Simulation studies have been carried out to investigate the performance of the parameters’ estimates. The results based on the real datasets and simulation studies provide evidence of better performance of the suggested distribution.

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