In this paper, we propose a new version of the Mirra distribution known as weighted Mirra distribution. Some of The different structural properties of the new model are studied such as moments, survival (Reliability) and hazard function, and order statistics, Moment generating function and Characteristic function. and the model parameters are estimated by maximum likelihood estimation likelihood estimation. Finally a real life data set has been analyzed, whereit is observed that the weighted Mirra distribution fit better to the data than the Mirra distribution.

1.
Fisher
,
R. A.
"
The effect of methods of ascertainment upon the estimation of frequencies
."
Annals of eugenics
6
.
1
(
1934
):
13
25
.
2.
Rao
,
C. R.
"
On discrete distributions arising out of methods of ascertainment
."
Sankhyā: The Indian Journal of Statistics, Series A
(
1965
):
311
324
.
3.
Zelen
,
M.
"
Problems in cell kinetic and the early detection of disease, in Reliability and Biometry
",
F. Proschan & R.
. (
1974
)
4.
Patil
,
G. P.
, and
C. R.
Rao
. "
Weighted distributions and size-biased sampling with applications to wildlife populations and human families
."
Biometrics
(
1978
):
179
189
.
5.
Gupta
,
R. C.
, and
J. P.
Keating
. "
Relations for reliability measures under length biased sampling
."
Scandinavian Journal of Statistics
(
1986
):
49
56
.
6.
Shi
,
X
,
B. O.
Oluyede
, and
Marvis
Pararai
. "
Theoretical Properties of the Weighted Generalized Rayleigh and Related Distributions
."
Theoretical Mathematics and Applications
2
.
2
(
2012
):
45
62
.
7.
Dey
,
S
, S.A, and
C.
Park
. "
Weighted exponential distribution: properties and different methods of estimation
."
Journal of Statistical Computation and Simulation
85
.
18
(
2015
):
3641
3661
.
8.
Kilany
,
N. M.
"
Weighted lomax distribution
."
SpringerPlus
5
.
1
(
2016
):
1
18
.
9.
Ayesha
,
A.
"
Size biased Lindley distribution and its properties a special case of weighted distribution
."
Applied Mathematics
8
.
06
(
2017
):
808
819
.
10.
Ajami
,
M.
, and
S. M. A.
Jahanshahi
. "
Parameter estimation in Weighted Rayleigh distribution
."
Journal of Modern Applied Statistical Methods
16
.
2
(
2017
):
14
.
11.
Para
,
B.A.
, &
Jan
,
T. R.
.
On three Parameter Weighted Pareto Type II Distribution: Properties and Applications in Medical Sciences
.
Applied Mathematics and Information Sciences Letters
,
6
(
1
), (
2018
),
13
26
.
12.
Sen
S
,
Ghosh
SK
,
Al–Mofleh
H.
The mirra distribution for modeling time–to event data set
.
In International Conference on Strategic Management, Decision Theory and Data Science
.
13.
Patil
,
G.P.
and
Ord
,
J.K.
(
1976
).
On Size-Biased Sampling and Related Form-Invariant Weighted Distributions
.
Industrial Journal of Statistics
,
38
(
1
),
48
61
.
14.
Abouammoh
,
A. M.
,
S. A.
Abdulghani
, and
I. S.
Qamber
. "
On partial orderings and testing of new better than renewal used classes
."
Reliability Engineering & System Safety
43
.
1
(
1994
):
37
41
.
This content is only available via PDF.
You do not currently have access to this content.