scholarly journals On The Estimation of Survival Function and Parameter Exponential Life Time Distribution

2009 ◽  
Vol 5 (2) ◽  
pp. 130-135
Author(s):  
Hadeel Salim Al-Kutubi ◽  
Noor Akma Ibrahim
Keyword(s):  
Time Distribution ◽  
Survival Function ◽  
Life Time

A general formula for the downtime distribution of a parallel system

1996 ◽  
Vol 33 (03) ◽  
pp. 772-785
Author(s):  
Harald Haukås ◽  
Terje Aven
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Time Distribution ◽  
Life Time ◽  
Exact Formula ◽  
Parallel System ◽  
System Failure ◽  
System Failures ◽  
Failure Scenario ◽  
Common Situation

In this paper we study the problem of computing the downtime distribution of a parallel system comprising stochastically identical components. It is assumed that the components are independent, with an exponential life-time distribution and an arbitrary repair time distribution. An exact formula is established for the distribution of the system downtime given a specific type of system failure scenario. It is shown by performing a Monte Carlo simulation that the portion of the system failures that occur as described by this scenario is close to one when we consider a system with quite available components, the most common situation in practice. Thus we can use the established formula as an approximation of the downtime distribution given system failure. The formula is compared with standard Markov expressions. Some possible extensions of the formula are presented.

Estimating life-time distribution by observing population continuously

2014 ◽  
Vol 79 ◽  
pp. 182-197 ◽  
Author(s):  
Hanhua Feng ◽  
Parijat Dube ◽  
Li Zhang
Keyword(s):  
Time Distribution ◽  
Life Time

A general formula for the downtime distribution of a parallel system

1996 ◽  
Vol 33 (3) ◽  
pp. 772-785 ◽  
Author(s):  
Harald Haukås ◽  
Terje Aven
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Time Distribution ◽  
Life Time ◽  
Exact Formula ◽  
Parallel System ◽  
System Failure ◽  
System Failures ◽  
Failure Scenario ◽  
Common Situation

In this paper we study the problem of computing the downtime distribution of a parallel system comprising stochastically identical components. It is assumed that the components are independent, with an exponential life-time distribution and an arbitrary repair time distribution. An exact formula is established for the distribution of the system downtime given a specific type of system failure scenario. It is shown by performing a Monte Carlo simulation that the portion of the system failures that occur as described by this scenario is close to one when we consider a system with quite available components, the most common situation in practice. Thus we can use the established formula as an approximation of the downtime distribution given system failure. The formula is compared with standard Markov expressions. Some possible extensions of the formula are presented.

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 Inverted Power Rama Distribution with Applications to Life Time Data

2020 ◽  
pp. 1-21
Author(s):  
Chrisogonus K. Onyekwere ◽  
George A. Osuji ◽  
Samuel U. Enogwe
Keyword(s):  
Heavy Tails ◽  
Survival Function ◽  
Real Life ◽  
Stochastic Ordering ◽  
Life Time ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Statistical Characteristics ◽  
Entropy Measure ◽  
Time Data

In this paper, we introduced the Inverted Power Rama distribution as an extension of the Inverted Rama distribution. This new distribution is capable of modeling real life data with upside down bathtub shape and heavy tails. Mathematical and statistical characteristics such as the quantile function, mode, moments and moment generating function, entropy measure, stochastic ordering and distribution of order statistics have been derived. Furthermore, reliability measures like survival function, hazard function and odds function have been derived. The method of maximum likelihood was used for estimating the parameters of the distribution. To demonstrate the applicability of the distribution, a numerical example was given. Based on the results, the proposed distribution performed better than the competing distributions.

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