Abstract
Uniformly minimum variance unbiased (UMVU) estimators of reliability function (both stress–strength and mission time) and the associated variance are derived for a class of generalization of Lindley distribution. The application of the results is further validated by a real data study.
Keywords
Get full access to this article
View all access options for this article.
References
1.
Lindley
DV.
Fiducial distributions and Bayes' theorem .
J R Stat Soc Series B
. 1958 ; 20 : 102 –107 .
2.
Ghitany
ME.
,
Atieh
B.
,
Nadarajah
S.
Lindley distribution and its application .
Math Comput Simul
. 2008 ; 78 : 493 –506 .
3.
Zakerzadah
H.
,
Dolati
A.
Generalized Lindley distribution .
J. Math Ext
. 2009 ; 3 (2 ): 1 –17 .
4.
Bakouch
HS.
,
Al-Zahrani
BM.
,
Al-Shomrani
AA.
,
Marchi
VA.
,
Louzada
F.
An extended Lindley distribution .
J Korean Stat Soc
. 2012 ; 41 : 75 –85 .
5.
Ghitany
M.
,
Merovci
F.
,
Elgarhy
M.
A new generalized Lindley distribution .
Math Theory Model
. 2013 ; 3 (13 ): 30 –47 .
6.
Shanker
R.
,
Sharma
S.
A two parameter Lindley distribution for modeling waiting and survival times data .
J. Appl Math
. 2013 ; 4 : 363 –368 .
7.
Bhati
D.
,
Malik
M.
,
Vaman
H.
Lindley: Exponential distribution—Properties and application .
Metron
. 2015 ; 73 (3 ): 335 –357 .
8.
Abouammoh
AM.
,
Alshangiti
AM.
,
Ragab
IE.
A new generalized Lindley distribution .
J Stat Comput Sim
. 2015 ; 85 (18 ): 3662 –3678 .
9.
Sharma
VK.
,
Khandelwal
P.
On the extension of inverse Lindley distribution .
J Data Sci
. 2017 ; 15 : 205 –220 .
10.
Abouelmagd
THM.
,
Al-Mualim
S.
,
Afify
AZ.
,
Ahmad
M.
,
Al-Mofleh
H.
The odd Lindley Burr XII distribution with applications .
Pak J Statis
. 2018 ; 34 (1 ): 15 –32 .
11.
Korkmaz
MC.
,
Yousof
HM.
,
Hamedani
GG.
The exponential Lindley odd log-logistic-G family: Properties, characterizations and applications .
J Stat Theory Appl
. 2018 ; 17 (3 ): 554 –571 .
12.
Bouchahed
L.
,
Zeghdoudi
H.
A new and unified approach in generalizing the Lindley's distribution with applications .
Stat Trans
. 2018 ; 19 (1 ): 61 –74 .
13.
Shanker
R.
Sujatha distribution and its applications .
Stat Trans New Series
. 2016 ; 17 (3 ): 391 –410 .
14.
Ayesha
A.
Size biased Lindley distribution and its properties a special case of weighted distribution .
J Appl Math
. 2017 ; 8 : 808 –819 .
15.
Al-Mutairi
Dk
Ghitany
ME.
,
Kundu
D.
Inference on stress: Strength reliability from Lindley distribution .
Commun Stat Theory Methods
. 2013 ; 42 , 1443 –1463 .
16.
Rohatgi
VK.
Saleh AKMD . An introduction to probability and statistics. 2nd edition. New York, NY: John Wiley & Sons ; 2000 .
17.
Tong
H.
A note on the estimation of P(Y <X), in the exponential case .
Technometrics
. 1974 ; 16 (4 ): 625 .
18.
Feller
W.
. An introduction to probability theory and its applications. Volume 2, 2nd edition. New York, NY: John Wiley & Sons ; 1971 .
