scholarly journals A New Extended Cosine—G Distributions for Lifetime Studies

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2758
Author(s):  
Mustapha Muhammad ◽  
Rashad A. R. Bantan ◽  
Lixia Liu ◽  
Christophe Chesneau ◽  
Muhammad H. Tahir ◽  
...  
Keyword(s):  
Weibull Distribution ◽  
Residual Life ◽  
Series Representation ◽  
Absolute Error ◽  
Quantile Function ◽  
Least Square ◽  
Cumulative Distribution ◽  
Reliability Parameter ◽  
Asymptotic Results ◽  
Error Loss

In this article, we introduce a new extended cosine family of distributions. Some important mathematical and statistical properties are studied, including asymptotic results, a quantile function, series representation of the cumulative distribution and probability density functions, moments, moments of residual life, reliability parameter, and order statistics. Three special members of the family are proposed and discussed, namely, the extended cosine Weibull, extended cosine power, and extended cosine generalized half-logistic distributions. Maximum likelihood, least-square, percentile, and Bayes methods are considered for parameter estimation. Simulation studies are used to assess these methods and show their satisfactory performance. The stress–strength reliability underlying the extended cosine Weibull distribution is discussed. In particular, the stress–strength reliability parameter is estimated via a Bayes method using gamma prior under the square error loss, absolute error loss, maximum a posteriori, general entropy loss, and linear exponential loss functions. In the end, three real applications of the findings are provided for illustration; one of them concerns stress–strength data analyzed by the extended cosine Weibull distribution.

scholarly journals The Generalized Ampadu-G Family of Distributions: Properties, Applications and Characterizations

2020 ◽  
pp. 139-167
Author(s):  
Clement Boateng Ampadu ◽  
Abdulzeid Yen Anafo
Keyword(s):  
Weibull Distribution ◽  
Density Function ◽  
Survival Function ◽  
Real Life ◽  
Life Time ◽  
Quantile Function ◽  
Cumulative Distribution ◽  
Model Parameters ◽  
New Family ◽  
Family Of Distributions

This paper introduces a new class of distributions called the generalized Ampadu-G (GA-G for short) family of distributions, and with a certain restriction on the parameter space, the family is shown to be a life-time distribution. The shape of the density function and hazard rate function of the GA-G family is described analytically. When G follows the Weibull distribution, the generalized Ampadu-Weibull (GA-W for short) is presented along with its hazard and survival function. Several sub-models of the GA-W family are presented. The transformation technique is applied to this new family of distributions, and we obtain the quantile function of the new family. Power series representations for the cumulative distribution function (CDF) and probability density function (PDF) are also obtained. The rth non-central moments, moment generating function, and Renyi entropy associated with the new family of distributions are derived. Characterization theorems based on two truncated moments and conditional expectation are also presented. A simulation study is also conducted, and we find that using the method of maximum likelihood to estimate model parameters is adequate. The GA-W family of distributions is shown to be practically significant in modeling real life data, and is shown to be superior to some non-trivial generalizations of the Weibull distribution. A further development concludes the paper.

scholarly journals The Generalized Gamma – Exponentiated Weibull Distribution with its Properties

2020 ◽  
Vol 31 (2) ◽  
pp. 30
Author(s):  
Salah Hamza Abid ◽  
Nadia Hashim Al-Noor ◽  
Mohammad Abd Alhussein Boshi
Keyword(s):  
Weibull Distribution ◽  
Simulated Data ◽  
Quantile Function ◽  
Cumulative Distribution ◽  
Generalized Gamma ◽  
Distribution Probability ◽  
Exponentiated Weibull Distribution ◽  
Exponentiated Weibull ◽  
Rate Functions ◽  
Special Case

In this paper, we present the Generalized Gamma-Exponentiated Weibull distribution as a special case of new generated Generalized Gamma - G family of probability distribution. The cumulative distribution, probability density, reliability and hazard rate functions are introduced. Furthermore, the most vital statistical properties, for instance, the r-th moment, characteristic function, quantile function, simulated data, Shannon and relative entropies besides the stress-strength model are obtained.

Interpretation of Graphs that Compare the Distribution Functions of Estimators

1990 ◽  
Vol 6 (1) ◽  
pp. 97-102 ◽  
Author(s):  
Brent R. Moulton
Keyword(s):  
Cumulative Distribution Function ◽  
Absolute Error ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Limited Information ◽  
One Dimensional ◽  
Error Loss ◽  
Least Squares Estimators ◽  
Squared Error ◽  
Exact Distributions

In this paper I examine graphical comparisons of one-dimensional (or marginal) distribution functions of alternative estimators. It is shown that areas under the c.d.f. (cumulative distribution function) curve can be given a decision-theoretic interpretation as risk under a bounded absolute-error loss function. I also show that by a simple rescaling of the graph's axes, graphical areas are created which can be interpreted as risk under bounded squared-error loss. The bounded loss functions are applied to compare graphically and numerically the risk of exact distributions of the limited-information maximum likelihood and two-stage least-squares estimators in a simultaneous equations model.

Determination of the Three-Parameter Weibull Distribution and Confidence Bands From Experimental Fatigue Strength Data

2004 ◽  
Author(s):  
Enayat Mahajerin ◽  
Gary Burgess
Keyword(s):  
Distribution Function ◽  
Fatigue Strength ◽  
Weibull Distribution ◽  
Structural Reliability ◽  
Confidence Bands ◽  
Least Square ◽  
Cumulative Distribution ◽  
Point Estimate ◽  
Cumulative Probability ◽  
Discrete Version

The S-N curve for the material used to make a pressure vessel is approximate because it is drawn from a limited number of test specimens. The resulting curve may be in error due to a variety of factors including surface condition, size, environment conditions, and stress concentrations. As a result, when the fatigue strength like the endurance limit is determined from the S-N curve by observing a definite break in the curve, it will be subject to error. Because of these uncertainties, it is necessary to use appropriate statistical methods to interpret the test results. In this paper, it is assumed that the percentage of failures for a given service life can be approximated by a three-parameter Weibull distribution. The Weibull distribution is flexible and has been shown to be suitable for structural reliability. The distribution is fitted to experimental data using a least square best fit approach applied to a discrete version of the cumulative probability distribution function, F(x). In practice a point-by-point estimate of the cumulative distribution function is used. As a result, it is necessary to establish confidence bands. The true curve of F(x) lies within these bands for a given probability.

scholarly journals A Discrete Analogue of the Continuous Marshall-Olkin Weibull Distribution with Application to Count Data

2020 ◽  
pp. 415-428
Author(s):  
Festus C. Opone ◽  
Elvis A. Izekor ◽  
Innocent U. Akata ◽  
Francis E. U. Osagiede
Keyword(s):  
Weibull Distribution ◽  
Survival Function ◽  
Probability Generating Function ◽  
Discrete Distribution ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Discrete Analogue ◽  
Cumulative Distribution ◽  
Probability Mass Function ◽  
Unknown Parameters

In this paper, we introduced the discrete analogue of the continuous Marshall-Olkin Weibull distribution using the discrete concentration approach. Some mathematical properties of the proposed discrete distribution such as the probability mass function, cumulative distribution function, survival function, hazard rate function, second rate of failure, probability generating function, quantile function and moments are derived. The method of maximum likelihood estimation is employed to estimate the unknown parameters of the proposed distribution. The applicability of the proposed discrete distribution was examined using an over-dispersed and under-dispersed data sets.

scholarly journals On predictive density estimation for location families under integrated absolute error loss

Bernoulli ◽  
2017 ◽  
Vol 23 (4B) ◽  
pp. 3197-3212 ◽  
Author(s):  
Tatsuya Kubokawa ◽  
Éric Marchand ◽  
William E. Strawderman
Keyword(s):  
Density Estimation ◽  
Absolute Error ◽  
Predictive Density ◽  
Error Loss

The Korteweg-de Vries equation and water waves. Solutions of the equation. Part 1

1973 ◽  
Vol 59 (4) ◽  
pp. 721-736 ◽  
Author(s):  
Harvey Segur
Keyword(s):  
Water Waves ◽  
Large Time ◽  
Vries Equation ◽  
Asymptotic Properties ◽  
Series Representation ◽  
Convergent Series ◽  
Asymptotic Results ◽  
De Vries ◽  
Method Of Solution

The method of solution of the Korteweg–de Vries equation outlined by Gardneret al.(1967) is exploited to solve the equation. A convergent series representation of the solution is obtained, and previously known aspects of the solution are related to this general form. Asymptotic properties of the solution, valid for large time, are examined. Several simple methods of obtaining approximate asymptotic results are considered.

scholarly journals Transmuted Probability Distributions: A Review

2020 ◽  
pp. 83-94
Author(s):  
Md. Mahabubur Rahman ◽  
Bander Al-Zahrani ◽  
Saman Hanif Shahbaz ◽  
Muhammad Qaiser Shahbaz
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Quantile Function ◽  
Cumulative Distribution ◽  
Functional Composition ◽  
Inverse Cumulative Distribution Function ◽  
Family Of Distributions

Transmutation is the functional composition of the cumulative distribution function (cdf) of one distribution with the inverse cumulative distribution function (quantile function) of another. Shaw and Buckley(2007), first apply this concept and introduced quadratic transmuted family of distributions. In this article, we have presented a review about the transmuted families of distributions. We have also listed the transmuted distributions, available in the literature along with some concluding remarks.

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