Modeling survival data depends on the shape of the hazard rate. In this paper, a distribution called the Extended Inverse Lindley distribution, will be introduced. Extended Inverse Lindley distribution is a distribution that is formed from the transformation of the two-parameter Lindley distribution. The transformations used are power transformation and inverse transformation. Thus, the Extended Inverse Lindley distribution can model heavy-tailed data with an upside-down bathtub hazard rate. In this essay, we discuss how to construct Extended Inverse Lindley distribution and characteristics of these distributions. These include the probability density function, cumulative distribution function, survival function, hazard rate, r-th moment, and mode. The parameters of the Extended Inverse Lindley distribution were estimated using the maximum likelihood method. At the end of this paper, the Extended Inverse Lindley distribution is used to illustrate the repairing time data (in hours) for 46 failures of an airborne communications receiver and shown that the Extended Inverse Lindley distribution is more suitable for modeling data than other distributions.

1.
D.
Collet
,
Modelling Survival Data in Medical Research,
2nd edition (
Springer
,
US
,
2003
).
2.
A.
Langlands
,
S.
Pocock
,
G.
Kerr
and
S.
Gore
,
British Medical J.
2
,
1247
1251
(
1997
).
3.
M. E.
Ghitany
,
B.
Atieh
and
S.
Nadarajah
,
Mathematics and Computers in Simulation
78
,
49
506
(
2007
).
4.
R.
Shanker
,
S.
Sharma
and
R.
Shanker
,
Applied Math.
4
,
363
368
(
2013
).
5.
V.K.
Sharma
,
S.K.
Singh
,
U.
Singh
and,
F.
Merovci
,
Com. Stat. Theory Methods
45
,
5709
5729
(
2015
).
6.
S.H.
Alkarni
,
Springer Plus.
4
,
690
(
2015
).
7.
J. F.
Lawless
,
Statistical Models and Methods for Lifetime Data
, 2nd edition (
John Wiley and Sons
,
Hoboken
,
2003
), p.
204
.
This content is only available via PDF.
You do not currently have access to this content.