scholarly journals Order Statistics of Additive Uniform Exponential Distribution

2021 ◽  
Vol 9 (10) ◽  
pp. 1084-1087
Author(s):  
Dr. Uppu Venkata Subbarao
Keyword(s):  
Order Statistics ◽  
Exponential Distribution ◽  
Order Statistic ◽  
Probability Density Functions ◽  
Joint Density ◽  
Density Functions ◽  
Length Of Service ◽  
Maximum Order ◽  
Minimum Order ◽  
Distribution Moments

Abstract: In this paper we investigated the order statistics by using Additive Uniform Exponential Distribution (AUED) proposed by Venkata Subbarao Uppu (2010).The probability density functions of rth order Statistics, lth moment of the rth order Statistic, minimum, maximum order statistics, mean of the maximum and minimum order statistics, the joint density function of two order statistics were calculated and discussed in detailed . Applications and several aspects were discussed Keywords: Additive Uniform Exponential Distribution, Moments, Minimum order statistic, Maximum order statistic, Joint density of the order Statistics, complete length of service.

scholarly journals On the Performance of Transmuted Logistic Distribution: Statistical Properties and Application

2019 ◽  
Vol 1 (3) ◽  
pp. 34-42
Author(s):  
Adeyinka Femi Samuel
Keyword(s):  
Biological Sciences ◽  
Probability Density ◽  
Order Statistics ◽  
Likelihood Estimation ◽  
Moment Generating Function ◽  
Probability Density Functions ◽  
Logistic Distribution ◽  
Density Functions ◽  
Maximum Order ◽  
Method Of Maximum Likelihood

In this article we transmute the logistic distribution using quadratic rank transmutation map to develop a transmuted logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its parent model to enhance more flexibility in the analysis of data in various disciplines such as biological sciences, actuarial science, finance and insurance. The mathematical properties such as moment generating function, quantile, median and characteristic function of this distribution are discussed. The probability density functions of the minimum and maximum order statistics of the transmuted logistic distribution are established and the relationships between the probability density functions of the minimum and maximum order statistics of the parent model and the probability density function of the transmuted logistic distribution are considered. The parameter estimation is done by the method of maximum likelihood estimation. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using it to fit relevant data. The study is concluded by demonstrating that the transmuted logistic distribution performs better than its parent model. 

Reliability Analysis of Shiplift Gear Based on System-Level Load-Strength Interference Model

2010 ◽  
Vol 118-120 ◽  
pp. 354-358
Author(s):  
Ying Wu ◽  
Li Yang Xie ◽  
De Cheng Wang ◽  
Ji Zhang Gao
Keyword(s):  
Reliability Analysis ◽  
Order Statistic ◽  
System Reliability ◽  
Bending Strength ◽  
High Reliability ◽  
Interference Model ◽  
System Level ◽  
Maximum Order ◽  
Minimum Order ◽  
Analysis System

A reliability analysis method for the shiplift gear according to the system-level load-strength interference model is presented. The gear is regarded as a series system with dependent failure and multiple failure models. Its reliability is obtained by calculating the probability that the minimum order statistic of the strengths exceeds the maximum order statistic of repeated random loads. The load probability distribution of gear is then obtained using Monte Carlo on the basis of load information. The contact strength and bending strength are calculated. On the basis of system-level load-strength interference analysis, system reliability of a gear is straightforward built up. Finally, system reliability of a gear is worked out, which shows a high reliability.

scholarly journals Probability Density Functions for Prediction Using Normal and Exponential Distribution

2021 ◽  
pp. 40-52
Author(s):  
Kunio Takezawa
Keyword(s):  
Probability Density Function ◽  
Normal Distribution ◽  
Probability Density ◽  
Density Function ◽  
Exponential Distribution ◽  
Predictive Ability ◽  
Probability Density Functions ◽  
Density Functions ◽  
Specific Distribution ◽  
Using Data

When data are found to be realizations of a specific distribution, constructing the probability density function based on this distribution may not lead to the best prediction result. In this study, numerical simulations are conducted using data that follow a normal distribution, and we examine whether probability density functions that have shapes different from that of the normal distribution can yield larger log-likelihoods than the normal distribution in the light of future data. The results indicate that fitting realizations of the normal distribution to a different probability density function produces better results from the perspective of predictive ability. Similarly, a set of simulations using the exponential distribution shows that better predictions are obtained when the corresponding realizations are fitted to a probability density function that is slightly different from the exponential distribution. These observations demonstrate that when the form of the probability density function that generates the data is known, the use of another form of the probability density function may achieve more desirable results from the standpoint of prediction.

The characterization of distributions by order statistics and record values — a unified approach

1984 ◽  
Vol 21 (2) ◽  
pp. 326-334 ◽  
Author(s):  
Paul Deheuvels
Keyword(s):  
Order Statistics ◽  
Exponential Distribution ◽  
Simple Proof ◽  
Order Statistic ◽  
Continuous Distribution ◽  
Record Values ◽  
Discrete Distributions ◽  
Unified Approach ◽  
Characterization Of Distributions

It is shown that, in some particular cases, it is equivalent to characterize a continuous distribution by properties of records and by properties of order statistics. As an application, we give a simple proof that if two successive jth record values and associated to an i.i.d. sequence are such that and are independent, then the sequence has to derive from an exponential distribution (in the continuous case). The equivalence breaks up for discrete distributions, for which we give a proof that the only distributions such that Xk, n and Xk+1, n – Xk, n are independent for some k ≧ 2 (where Xk, n is the kth order statistic of X1, ···, Xn) are degenerate.

The characterization of distributions by order statistics and record values — a unified approach

1984 ◽  
Vol 21 (02) ◽  
pp. 326-334
Author(s):  
Paul Deheuvels
Keyword(s):  
Order Statistics ◽  
Exponential Distribution ◽  
Simple Proof ◽  
Order Statistic ◽  
Continuous Distribution ◽  
Record Values ◽  
Discrete Distributions ◽  
Unified Approach ◽  
Characterization Of Distributions

It is shown that, in some particular cases, it is equivalent to characterize a continuous distribution by properties of records and by properties of order statistics. As an application, we give a simple proof that if two successivejth record valuesandassociated to an i.i.d. sequence are such thatandare independent, then the sequence has to derive from an exponential distribution (in the continuous case). The equivalence breaks up for discrete distributions, for which we give a proof that the only distributions such thatXk, nandXk+1,n–Xk, nare independent for somek≧ 2 (whereXk, nis thekth order statistic ofX1, ···,Xn) are degenerate.

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