The Estimation of Reliability from Stress–Strength for Exponentiated Frechet Distribution

2017 ◽  
Vol 43 (3) ◽  
pp. 863-874
Author(s):  
M. M. Badr ◽  
A. I. Shawky ◽  
A. H. Alharby
Keyword(s):  
Fréchet Distribution ◽  
Frechet Distribution

Properties and methods of estimation for a bivariate exponentiated Fréchet distribution

2020 ◽  
Vol 70 (5) ◽  
pp. 1211-1230
Author(s):  
Abdus Saboor ◽  
Hassan S. Bakouch ◽  
Fernando A. Moala ◽  
Sheraz Hussain
Keyword(s):  
Maximum Likelihood ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Superior Performance ◽  
Estimation Methods ◽  
Conditional Probability Density ◽  
Data Set ◽  
Fréchet Distribution ◽  
Frechet Distribution

AbstractIn this paper, a bivariate extension of exponentiated Fréchet distribution is introduced, namely a bivariate exponentiated Fréchet (BvEF) distribution whose marginals are univariate exponentiated Fréchet distribution. Several properties of the proposed distribution are discussed, such as the joint survival function, joint probability density function, marginal probability density function, conditional probability density function, moments, marginal and bivariate moment generating functions. Moreover, the proposed distribution is obtained by the Marshall-Olkin survival copula. Estimation of the parameters is investigated by the maximum likelihood with the observed information matrix. In addition to the maximum likelihood estimation method, we consider the Bayesian inference and least square estimation and compare these three methodologies for the BvEF. A simulation study is carried out to compare the performance of the estimators by the presented estimation methods. The proposed bivariate distribution with other related bivariate distributions are fitted to a real-life paired data set. It is shown that, the BvEF distribution has a superior performance among the compared distributions using several tests of goodness–of–fit.

New Acceptance Sampling Plans Based on Percentiles for Exponentiated Fréchet Distribution

2016 ◽  
Vol 31 (1) ◽  
Author(s):  
Gadde Srinivasa Rao ◽  
Kanaparthi Rosaiah ◽  
Mothukuri Sridhar Babu ◽  
Devireddy Charanaudaya Sivakumar
Keyword(s):  
Operating Characteristic ◽  
Real Data ◽  
Acceptance Sampling ◽  
Producer’S Risk ◽  
Data Set ◽  
Sampling Plans ◽  
Fréchet Distribution ◽  
Acceptance Sampling Plans ◽  
Characteristic Values ◽  
Frechet Distribution

AbstractIn this article, acceptance sampling plans are developed for the exponentiated Fréchet distribution based on percentiles when the life test is truncated at a pre-specified time. The minimum sample size necessary to ensure the specified life percentile is obtained under a given customer's risk and producer's risk simultaneously. The operating characteristic values of the sampling plans are presented. One example with real data set is also given as an illustration.

Extreme value statistics of interval maximum amplitudes due to aftershocks and its application for early forecast

2021 ◽  
Author(s):  
Kaoru Sawazaki
Keyword(s):  
Early Period ◽  
Maximum Amplitude ◽  
Large Earthquake ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Earthquake Catalog ◽  
Aftershock Activity ◽  
Fréchet Distribution ◽  
Single Station ◽  
Frechet Distribution

<p>Waveforms from many aftershocks occurring immediately after a large earthquake tend to overlap in a seismogram, which makes it difficult to pick their P- and S-wave phases. Accordingly, to determine hypocenter and magnitude of the aftershocks becomes difficult and thereby causes deterioration of earthquake catalog. Using such deteriorated catalog may cause misevaluation of ongoing aftershock activity. Since aftershock activity is usually most intense in the early period after a large earthquake, requirement of early aftershock forecast and deterioration of the aftershock catalog are impatient.</p><p>Several methods for aftershock forecast, using deteriorated automatic earthquake catalog (Omi et al., 2016, 2019) or continuous seismic envelopes (Lippiello et al., 2016), have been proposed to overcome such a situation. In this study, I propose another method that evaluates excess probability of maximum amplitude (EPMA) due to aftershocks using a continuous seismogram. The proposed method is based on the extreme value statistics, which provides probability distribution of maximum amplitudes within constant time intervals. From the Gutenberg-Richter and the Omori-Utsu laws and a conventional ground motion prediction equation (GMPE), I derived this interval maximum amplitude (IMA) follows the Frechet distribution (or type Ⅱ extreme-value distribution). Using the Monte-Carlo based approach, I certified that this distribution is well applicable to IMAs and available for forecasting maximum amplitudes even if many seismograms are overlapped.</p><p>Applying the Frechet distribution to the first 3 hour-long seismograms of the 2008 Iwate-Miyagi Nairiku earthquake (M<sub>W</sub> 6.9), Japan, I computed the EPMAs for 4 days at 4 stations. The maximum amplitudes due to experienced aftershocks proceeded following mostly within the 10 % to 90 % EPMA curves. This performance may be acceptable for a practical use.</p><p>Differently from the catalog-based method, the proposed method is almost unaffected by overlap of seismograms even in early lapse times. Since it is based on a single station processing, even seismic “network” is not required, and can be easily deployed at locations of poor seismic network coverage. So far, this method is correctly applicable for typical mainshock-aftershock (Omori-Utsu-like) sequence only. However, potentially, it could be extended to multiple sequences including secondary aftershocks and remotely triggered earthquakes.</p>

Truncated Weibull Frèchet Distribution: Statistical Inference and Applications

2019 ◽  
Vol 16 (1) ◽  
pp. 52-60 ◽  
Author(s):  
Amal S. Hassan ◽  
M. Elgarhy ◽  
Said G. Nassr ◽  
Zubair Ahmad ◽  
Sharifah Alrajhi
Keyword(s):  
Statistical Inference ◽  
Fréchet Distribution ◽  
Frechet Distribution
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