The zero-truncated negative binomial-Erlang distribution is introduced. It is developed from negative binomial-Erlang distribution. In this work, the probability mass function is derived and some properties are included. The parameters of the zero-truncated negative binomial-Erlang distribution are estimated by using the maximum likelihood estimation. Finally, the proposed distribution is applied to real data, the number of methamphetamine in the Bangkok, Thailand. Based on the results, it shows that the zero-truncated negative binomial-Erlang distribution provided a better fit than the zero-truncated Poisson, zero-truncated negative binomial, zero-truncated generalized negative-binomial and zero-truncated Poisson-Lindley distributions for this data.

1.
R.
Winkelmann
, noop
Econometric analysis of count data
(
Springer Science and Business Media
,
2008
).
2.
M.
Greenwood
and
G. U.
Yule
, noop
Journal of the Royal statistical society
83
,
255
279
(
1920
).
3.
N. L.
Johnson
,
A. W.
Kemp
, and
S.
Kotz
, noop
Univariate discrete distributions
, Vol.
444
(
John Wiley and Sons
,
2005
).
4.
S.
Meng
,
W.
Yuan
, and
G.
Whitmore
, noop
Astin Bulletin
29
,
327
337
(
1999
).
5.
E.
Gómez-Déniz
,
J. M.
Sarabia
, and
E.
Caldeŕın-Ojeda
, noop
Insurance: Mathematics and Economics
42
,
39
49
(
2008
).
6.
H.
Zamani
and
N.
Ismail
, noop
Journal of Mathematics and Statistics
6
,
4
9
(
2010
).
7.
C.
Pudprommarat
,
W.
Bodhisuwan
, and
P.
Zeephongsekul
, noop
Journal of Applied Sciences
12
,
1853
1858
(
2012
).
8.
S.
Kongrod
,
W.
Bodhisuwan
, and
P.
Payakkapong
, noop
International Journal of Pure and Applied Mathematics
92
,
389
401
(
2014
).
9.
I.
Rocchetti
,
J.
Bunge
, and
D.
Böhning
, noop
The Annals of Applied Statistics
1512
1533
(
2011
).
10.
F.
David
and
N.
Johnson
, noop
Biometrics
8
,
275
285
(
1952
).
11.
M.
Sampford
,
Biometrika
42
,
58
69
(
1955
).
12.
X.
Ding
, noop HKU Theses Online (HKUTO) (
2015
).
13.
M. E.
Ghitany
,
D. K.
Al-Mutairi
, and
S.
Nadarajah
, noop
Math. Comput. Simul.
79
,
279
287
December (
2008
).
14.
F.
David
and
N.
Johnson
, noop
Biometrics
8
,
275
285
(
1952
).
15.
R Core Team
, R: A Language and Environment for Statistical Computing,
R Foundation for Statistical Computing
,
Vi-enna
,
Austria
(
2016
).
16.
H.
Akaike
, noop
IEEE transactions on automatic control
19
,
716
723
(
1974
).
17.
G.
Schwarz
, noop
The Annals of Statistics
6
,
461
464
(
1978
).
18.
T. B.
Arnold
and
J. W.
Emerson
, noop
R Journal
3
(
2011
).
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