Journal of the Iranian Statistical Society
پژوهشنامه انجمن آمار ایران
JIRSS
Basic Sciences
http://jirss.irstat.ir
1
admin
1726-4057
2538-189X
8
10.29252/jirss
14
1726-4057
13
en
jalali
1399
3
1
gregorian
2020
6
1
19
1
online
1
fulltext
en
Accurate Inference for the Mean of the Poisson-Exponential Distribution
62Fxx: Parametric inference
62Fxx: Parametric inference
Original Paper
Original Paper
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<p>Although the random sum distribution has been well-studied in probability theory, inference for the mean of such distribution is very limited in the literature. In this paper, two approaches are proposed to obtain inference for the mean of the Poisson-Exponential distribution. Both proposed approaches require the log-likelihood function of the Poisson-Exponential distribution, but the exact form of the log-likelihood function is not available. An approximate form of the log-likelihood function is then derived by the saddlepoint method. Inference for the mean of the Poisson-Exponential distribution can either be obtained from the modified signed likelihood root statistic or from the Bartlett corrected likelihood ratio statistic. The explicit form of the modified signed likelihood root statistic is derived in this paper, and a systematic method to numerically approximate the Bartlett correction factor, hence the Bartlett corrected likelihood ratio statistic is proposed. Simulation studies show that both methods are extremely accurate even when the sample size is small.</p>
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Bartlett Correction, p-value Punction, Saddlepoint Approximation, Signed Likelihood Root.
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http://jirss.irstat.ir/browse.php?a_code=A-11-716-1&slc_lang=en&sid=1
Wei
Lin
becky@utstat.toronto.edu
`10031947532846003390`

10031947532846003390
Yes
Department of Mathematics and Statistics, Thompson Rivers University, 805 TRU Way, Kamloops, British Columbia, Canada V2C 0C8.
Xiang
Li
lovedaershou@126.com
`10031947532846003391`

10031947532846003391
No
Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3.
Augustine
Wong
august@yorku.ca
`10031947532846003392`

10031947532846003392
No
Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3.