In this paper, a new family of distributions are introduced biased on Weibull Lindley (WL) distribution and arbitrary cumulative distribution function (CDF). This family is called Weibull Lindley general family of distributions (WLGFD). On this approach, we derive the Weibull Lindley Pareto distribution (WLPD). Several properties are included, PDF,CDF, moment generating function, hazard rate, reversed hazard function, odd function, quantile function, order statistics and moments are proved of the WLPD. An estimation procedure by the method of maximum likelihood, fisher matrix and a simulation are studied of WLPD. Finally, we give graph of PDF, CDF, mean squared error and bias at different values of parameters.

1.
A. Z.
Afifya
,
G. M.
Cordeiro
,
H. M.
Yousof
, Z. M., Nofal, and
A.
Alzaatreh
,
The kumaraswamy transmuted-g family of distributions: properties and applications
.
Journal of Data Science
,
14
(
2
),
245
270
, (
2016
).
2.
Z.
Ahmad
,
M.
Elgarhy
, and
G.
Hamedani
,
A new Weibull X family of distributions: properties, characterizations and applications
.
Journal of Statistical Distributions and Applications
,
5
(
1
):
1
18
, (
2018
).
3.
A.
Asgharzadeh
,
S.
Nadarajah
, and
F.
Sharafi
,
Weibull lindley distribution
.
REVSTAT Statistical Journal
,
16
:
87
113
, (
2018
).
4.
M.
Bourguignon
,
R. B.
Silva
and
G. M.
Cordeiro
,
The weibull-g family of probability distributions
.
Journal of data science
,
12
(
1
):
53
68
, (
2014
).
5.
S.
Dey
,
V. K..
Sharma
, and
M.
Mesfioui
,
A new extension of Weibull distribution with application to lifetime data
.
Annals of Data Science
,
4
(
1
):
31
61
, (
2017
).
6.
J.
Falgore
,
S.
Doguwa
, and
A.
Isah
,
The weibull-inverse lomax distribution with application on bladder cancer
.
Biometrics & Biostatistics International Journal
,
8
(
5
):
195
202
, (
2019
).
7.
F. S.
Gomes-Silva
,
A.
Percontini
,
E.
de Brito
,
M. W.
Ramos
,
R.
Venancio
, and
G. M.
Cordeiro
,
The odd lindley-g family of distributions
.
Austrian Journal of Statistics
,
46
(
1
):
65
87
, (
2017
).
8.
A. S.
Hassan
,
I.
Elbatal
, and,
S. E.
Hemeda
,
Weibull quasi Lindley distribution and its statistical properties with applications to lifetime data
.
International Journal of Applied Mathematics and Statistics
,
55
(
3
):
63
80
, (
2016
).
9.
A. S.
Hassan
, and
R. E.
Mohamed
,
Weibull inverse lomax distribution
.
Pakistan Journal of Statistics and Operation Research
,
587-603
, (
2019
).
10.
B.
Hosseini
,
M.
Afshari
, and
M.
Alizadeh
,
The generalized odd gamma-g family of distributions: properties and applications
.
Austrian Journal of Statistics
,
47
(
2
):
69
89
, (
2018
).
11.
M. C.
Korkmaz
,
E.
Altun
,
H. M.
Yousof
, and
G. G.
Hamedani
,
The odd power lindley generator of probability distributions: properties, characterizations and regression modeling
.
International Journal of Statistics and Probability.
8
,
1
22
;
2019
.
12.
A.
Mahdavi
, and
D.
Kundu
,
A new method for generating distributions with an application to exponential distribution
.
Communications in Statistics-Theory and Methods
,
46
(
13
):
6543
6557
, (
2017
).
13.
F.
Merovci
,
M.
Alizadeh
,
H. M.
Yousof
, and
G.
Hamedani
,
The exponentiated transmuted-g family of distributions: theory and applications
.
Communications in Statistics-Theory and Methods
,
46
(
21
):
10800
10822
, (
2017
).
14.
M.
Nasir
,
M.
Aljarrah
,
F.
Jamal
, and
M.
Tahir
,
A new generalized burr family of distributions based on quantile function
.
Journal of Statistics Applications and Probability
,
6
(
3
):
1
14
,, (
2017
).
15.
M.
Nasir
,
F.
Jamal
,
G. O.
Silva
, and
M.
Tahir
,
Odd burrg poisson family of distributions
.
Journal of Statistics Applications and Probability
,
7
(
1
):
9
28
, (
2018
).
16.
H. I.
Okagbue
,
M. O.
Adamu
, and
T. A.
Anake
,
Solutions of chi-square quantile differential equation
,
Proceedings of the World Congress on Engineering and Computer Science
,
San Francisco, USA
,
2017
,
25
-
27
,(2017).
17.
B. O.
Oluyede
,
G.
Warahena-Liyanage
, and
M.
Pararai
,
A new compound class of log-logistic weibull-poisson distribution: model, properties and applications
.
Journal of Statistical Computation and Simulation
,
86
(
7
):
1363
1391
, (
2016
).
18.
M. H.
Tahir
,
G. M.
Cordeiro
,
M.
Alizadeh
,
M.
Mansoor
,
M.
Zubair
, and
G. G.
Hamedani
,
The odd generalized exponential family of distributions with applications
.
Journal of Statistical Distributions and Applications
,
2
(
1
):
1
28
, (
2015
).
19.
N. J.
Hassan
,
H. Ghdhaib
Kalt
,
H. A.
Aal-Rkhais
and
A. E.
Hashoosh
,
The Weibull Lindley: General family of probability Distributions
MATHEMATICS IN ENGINEERING, SCIENCE AND AEROSPACE
,
12
,
1
14
(
2021
).
20.
A.
UlHaq
, and
M.
Elgarhy
,
The odd frchet-g family of probability distributions
.
Journal of Statistics Applications & Probability
,
7
(
1
):
185
201
, (
2018
).
21.
E.
Brito
,
G.
Cordeiro
,
H.
Yousof
,
M.
Alizadeh
, and
G.
Silva
,
The topp-leone odd log-logistic family of distributions
.
Journal of Statistical Computation and Simulation
,
87
(
15
):
3040
3058
,, (
2017
).
This content is only available via PDF.
You do not currently have access to this content.