Parameters estimation and application of generalized exponential distribution under grouped and right-censored data

doi:10.3868/s140-DDD-023-0013-x

Front. Math. China

2023, Vol. 18

Issue (3) : 165-174 https://doi.org/10.3868/s140-DDD-023-0013-x

RESEARCH　ARTICLE

Parameters estimation and application of generalized exponential distribution under grouped and right-censored data

Yuzhu TIAN^1,²(

), Maozai TIAN², Ping CHEN³

¹. Center for Applied Statistics, Renmin University of China, Beijing 100872, China
². School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, China
³. Dependment of Mathematics, Southeast University, Nanjing 210096, China

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Abstract

Generalized exponential distribution is a class of important distribution in lifedata analysis, especially in some skewed lifedata. The Parameter estimation problem for generalized exponential distribution model with grouped and right-censored data is considered. The maximum likelihood estimators are obtained using the EM algorithm. Some simulations are carried out to illustrate that the proposed algorithm is effective for the model. Finally, a set of medicine data is analyzed by generalized exponential distribution.

Keywords Generalized exponential distribution grouped and right-censored data EM algorithm

Corresponding Author(s): Yuzhu TIAN

Online First Date: 16 November 2023 Issue Date: 07 December 2023

Cite this article:

Yuzhu TIAN,Maozai TIAN,Ping CHEN. Parameters estimation and application of generalized exponential distribution under grouped and right-censored data[J]. Front. Math. China, 2023, 18(3): 165-174.

URL:

https://academic.hep.com.cn/fmc/EN/10.3868/s140-DDD-023-0013-x
https://academic.hep.com.cn/fmc/EN/Y2023/V18/I3/165

$η = (α, λ)$	n	s	$α^$	$λ^$
	60	100	1.4619	6.0934E?2
		200	1.4753	6.0963E?2
		500	1.4960	6.2527E?2
	120	100	1.5248	6.1241E?2
		200	1.5307	6.1609E?2
		500	1.5450	6.1889E?2
(1.5,0.06)	200	100	1.5168	6.1106E?2
		200	1.5345	6.1624E?2
		500	1.5423	6.1427E?2
	500	100	1.5260	6.0886E?2
		200	1.5257	6.0722E?2
		500	1.5267	6.0750E?2
	1000	100	1.5259	6.0643E?2
		200	1.5239	6.0552E?2
		500	1.5256	6.0557E?2

Tab.1 Parameter estimates (mean) for the generalized exponential distribution under data grouping and right censored data

$η = (α, λ)$	n	s	$α^$	$λ^$
	60	100	1.4163E?1	3.0760E?4
		200	1.1328E?1	2.1400E?4
		500	1.3976E?1	1.5213E?4
	120	100	2.9459E?2	5.1965E?5
		200	2.7928E?2	5.1485E?5
		500	3.8678E?2	4.9290E?5
(1.5,0.06)	200	100	1.2899E?2	3.6575E?5
		200	1.4822E?2	3.2750E?5
		500	1.3759E?2	2.9961E?5
	500	100	5.1914E?3	1.4735E?5
		200	3.9203E?3	1.2837E?5
		500	3.8831E?3	1.2434E?5
	1000	100	1.6000E?3	7.1194E?6
		200	1.6385E?3	6.3407E?6
		500	1.6379E?3	6.3476E?6

Tab.2 Parameter estimation mean square error (mse) for the generalized exponential distribution under data grouping and right censored data

Interval $I j$	Death numbers $D j$	Outfollowed numbers $W j$
1	456	0
2	226	39
3	152	22
4	171	23
5	135	24
6	125	107
7	83	133
8	74	102
9	51	68
10	42	64
11	43	45
12	34	53
13	18	33
14	9	27
15	6	23
16	0	0

Tab.3 Survival data of male patients with angina pectoris

Fig.1 Plot of the survival function and hazard rate function in male patients with angina pectoris

α^= 0.769 < 1

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