A study on methods for estimating the PDF and the CDF in the exponentiated gamma distribution

The exponentiated gamma distribution is a two parameters lifetime distribution with monotone and non-monotone failure rates. In this article, some estimation methods of the probability density function and the cumulative distribution function of the exponentiated gamma distribution such as uniformly...

Full description

Saved in:
Bibliographic Details
Published in:Communications in statistics. Simulation and computation 2020-08, Vol.49 (8), p.1999-2013
Main Author: Rasekhi, Mahdi
Format: Article
Language:English
Subjects:
Computer simulation
Distribution functions
Exponentiated gamma distribution
Failure rates
Least squares
Least squares estimator
Maximum likelihood estimator
Minimum distance estimator
Probabilistic methods
Probability density functions
Probability distribution functions
Statistical analysis
Uniformly minimum variance unbiased estimator
Weighted least squares estimator
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c338t-ed5363550d476888830695d3e17a21f7e39652c6097e5e2b97a24d4eeffced3e3
cites cdi_FETCH-LOGICAL-c338t-ed5363550d476888830695d3e17a21f7e39652c6097e5e2b97a24d4eeffced3e3
container_end_page 2013
container_issue 8
container_start_page 1999
container_title Communications in statistics. Simulation and computation
container_volume 49
creator Rasekhi, Mahdi
description The exponentiated gamma distribution is a two parameters lifetime distribution with monotone and non-monotone failure rates. In this article, some estimation methods of the probability density function and the cumulative distribution function of the exponentiated gamma distribution such as uniformly minimum variance unbiased (UMVU), maximum likelihood (ML), least squares, weighted least squares and Minimum distance estimators are studied and their performances through numerical simulations are compared. By the mean integrated squared error (MISE), the UMVU and ML are approximately equivalent and more efficient than the others based on simulation studies when the sample size is more than 40. A real data set is analyzed for illustrative purposes.
doi_str_mv 10.1080/03610918.2018.1508707
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2439239758</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2439239758</sourcerecordid><originalsourceid>FETCH-LOGICAL-c338t-ed5363550d476888830695d3e17a21f7e39652c6097e5e2b97a24d4eeffced3e3</originalsourceid><addsrcrecordid>eNp9kEFPwyAUx4nRxDn9CCYknqtQSktvLtOpyRI96NEQVl43lhUm0Oi-vXSbVznAP-T33oMfQteU3FIiyB1hJSU1Fbc5SRvlRFSkOkEjylmeFbSgp2g0MNkAnaOLENaEECYKMUKfExxir3fYWdxBXDkdcOs8hhBNp6KxSxxXgN8eZlhZvc_TlI3dR_jZOgs2GhVB46XqOoW1CdGbRR-Ns5forFWbAFfHc4w-Zo_v0-ds_vr0Mp3Ms4YxETPQnJWMc6KLqhRpMVLWXDOglcppWwGrS543Jakr4JAv6nRd6AKgbRtIGBujm0PfrXdffXq7XLve2zRS5gWrc1ZXXCSKH6jGuxA8tHLr0yf9TlIiB5Pyz6QcTMqjyVR3f6gzNqnp1LfzGy2j2m2cb72yjQmS_d_iF3oEeUw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2439239758</pqid></control><display><type>article</type><title>A study on methods for estimating the PDF and the CDF in the exponentiated gamma distribution</title><source>Taylor and Francis Science and Technology Collection</source><creator>Rasekhi, Mahdi</creator><creatorcontrib>Rasekhi, Mahdi</creatorcontrib><description>The exponentiated gamma distribution is a two parameters lifetime distribution with monotone and non-monotone failure rates. In this article, some estimation methods of the probability density function and the cumulative distribution function of the exponentiated gamma distribution such as uniformly minimum variance unbiased (UMVU), maximum likelihood (ML), least squares, weighted least squares and Minimum distance estimators are studied and their performances through numerical simulations are compared. By the mean integrated squared error (MISE), the UMVU and ML are approximately equivalent and more efficient than the others based on simulation studies when the sample size is more than 40. A real data set is analyzed for illustrative purposes.</description><identifier>ISSN: 0361-0918</identifier><identifier>EISSN: 1532-4141</identifier><identifier>DOI: 10.1080/03610918.2018.1508707</identifier><language>eng</language><publisher>Philadelphia: Taylor &amp; Francis</publisher><subject>Computer simulation ; Distribution functions ; Exponentiated gamma distribution ; Failure rates ; Least squares ; Least squares estimator ; Maximum likelihood estimator ; Minimum distance estimator ; Probabilistic methods ; Probability density functions ; Probability distribution functions ; Statistical analysis ; Uniformly minimum variance unbiased estimator ; Weighted least squares estimator</subject><ispartof>Communications in statistics. Simulation and computation, 2020-08, Vol.49 (8), p.1999-2013</ispartof><rights>2018 Taylor &amp; Francis Group, LLC 2018</rights><rights>2018 Taylor &amp; Francis Group, LLC</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c338t-ed5363550d476888830695d3e17a21f7e39652c6097e5e2b97a24d4eeffced3e3</citedby><cites>FETCH-LOGICAL-c338t-ed5363550d476888830695d3e17a21f7e39652c6097e5e2b97a24d4eeffced3e3</cites><orcidid>0000-0003-4836-7461</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Rasekhi, Mahdi</creatorcontrib><title>A study on methods for estimating the PDF and the CDF in the exponentiated gamma distribution</title><title>Communications in statistics. Simulation and computation</title><description>The exponentiated gamma distribution is a two parameters lifetime distribution with monotone and non-monotone failure rates. In this article, some estimation methods of the probability density function and the cumulative distribution function of the exponentiated gamma distribution such as uniformly minimum variance unbiased (UMVU), maximum likelihood (ML), least squares, weighted least squares and Minimum distance estimators are studied and their performances through numerical simulations are compared. By the mean integrated squared error (MISE), the UMVU and ML are approximately equivalent and more efficient than the others based on simulation studies when the sample size is more than 40. A real data set is analyzed for illustrative purposes.</description><subject>Computer simulation</subject><subject>Distribution functions</subject><subject>Exponentiated gamma distribution</subject><subject>Failure rates</subject><subject>Least squares</subject><subject>Least squares estimator</subject><subject>Maximum likelihood estimator</subject><subject>Minimum distance estimator</subject><subject>Probabilistic methods</subject><subject>Probability density functions</subject><subject>Probability distribution functions</subject><subject>Statistical analysis</subject><subject>Uniformly minimum variance unbiased estimator</subject><subject>Weighted least squares estimator</subject><issn>0361-0918</issn><issn>1532-4141</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kEFPwyAUx4nRxDn9CCYknqtQSktvLtOpyRI96NEQVl43lhUm0Oi-vXSbVznAP-T33oMfQteU3FIiyB1hJSU1Fbc5SRvlRFSkOkEjylmeFbSgp2g0MNkAnaOLENaEECYKMUKfExxir3fYWdxBXDkdcOs8hhBNp6KxSxxXgN8eZlhZvc_TlI3dR_jZOgs2GhVB46XqOoW1CdGbRR-Ns5forFWbAFfHc4w-Zo_v0-ds_vr0Mp3Ms4YxETPQnJWMc6KLqhRpMVLWXDOglcppWwGrS543Jakr4JAv6nRd6AKgbRtIGBujm0PfrXdffXq7XLve2zRS5gWrc1ZXXCSKH6jGuxA8tHLr0yf9TlIiB5Pyz6QcTMqjyVR3f6gzNqnp1LfzGy2j2m2cb72yjQmS_d_iF3oEeUw</recordid><startdate>20200802</startdate><enddate>20200802</enddate><creator>Rasekhi, Mahdi</creator><general>Taylor &amp; Francis</general><general>Taylor &amp; Francis Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0003-4836-7461</orcidid></search><sort><creationdate>20200802</creationdate><title>A study on methods for estimating the PDF and the CDF in the exponentiated gamma distribution</title><author>Rasekhi, Mahdi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c338t-ed5363550d476888830695d3e17a21f7e39652c6097e5e2b97a24d4eeffced3e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Computer simulation</topic><topic>Distribution functions</topic><topic>Exponentiated gamma distribution</topic><topic>Failure rates</topic><topic>Least squares</topic><topic>Least squares estimator</topic><topic>Maximum likelihood estimator</topic><topic>Minimum distance estimator</topic><topic>Probabilistic methods</topic><topic>Probability density functions</topic><topic>Probability distribution functions</topic><topic>Statistical analysis</topic><topic>Uniformly minimum variance unbiased estimator</topic><topic>Weighted least squares estimator</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Rasekhi, Mahdi</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical &amp; Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Communications in statistics. Simulation and computation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Rasekhi, Mahdi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A study on methods for estimating the PDF and the CDF in the exponentiated gamma distribution</atitle><jtitle>Communications in statistics. Simulation and computation</jtitle><date>2020-08-02</date><risdate>2020</risdate><volume>49</volume><issue>8</issue><spage>1999</spage><epage>2013</epage><pages>1999-2013</pages><issn>0361-0918</issn><eissn>1532-4141</eissn><abstract>The exponentiated gamma distribution is a two parameters lifetime distribution with monotone and non-monotone failure rates. In this article, some estimation methods of the probability density function and the cumulative distribution function of the exponentiated gamma distribution such as uniformly minimum variance unbiased (UMVU), maximum likelihood (ML), least squares, weighted least squares and Minimum distance estimators are studied and their performances through numerical simulations are compared. By the mean integrated squared error (MISE), the UMVU and ML are approximately equivalent and more efficient than the others based on simulation studies when the sample size is more than 40. A real data set is analyzed for illustrative purposes.</abstract><cop>Philadelphia</cop><pub>Taylor &amp; Francis</pub><doi>10.1080/03610918.2018.1508707</doi><tpages>15</tpages><orcidid>https://orcid.org/0000-0003-4836-7461</orcidid></addata></record>
fulltext fulltext
identifier ISSN: 0361-0918
ispartof Communications in statistics. Simulation and computation, 2020-08, Vol.49 (8), p.1999-2013
issn 0361-0918
1532-4141
language eng
recordid cdi_proquest_journals_2439239758
source Taylor and Francis Science and Technology Collection
subjects Computer simulation
Distribution functions
Exponentiated gamma distribution
Failure rates
Least squares
Least squares estimator
Maximum likelihood estimator
Minimum distance estimator
Probabilistic methods
Probability density functions
Probability distribution functions
Statistical analysis
Uniformly minimum variance unbiased estimator
Weighted least squares estimator
title A study on methods for estimating the PDF and the CDF in the exponentiated gamma distribution
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-28T07%3A55%3A12IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20study%20on%20methods%20for%20estimating%20the%20PDF%20and%20the%20CDF%20in%20the%20exponentiated%20gamma%20distribution&rft.jtitle=Communications%20in%20statistics.%20Simulation%20and%20computation&rft.au=Rasekhi,%20Mahdi&rft.date=2020-08-02&rft.volume=49&rft.issue=8&rft.spage=1999&rft.epage=2013&rft.pages=1999-2013&rft.issn=0361-0918&rft.eissn=1532-4141&rft_id=info:doi/10.1080/03610918.2018.1508707&rft_dat=%3Cproquest_cross%3E2439239758%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c338t-ed5363550d476888830695d3e17a21f7e39652c6097e5e2b97a24d4eeffced3e3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2439239758&rft_id=info:pmid/&rfr_iscdi=true