The main feature of survival data is that they are not symmetrically distributed and the end point of interest are not observed for some individuals leading to censoring situation. The presence of censoring makes this domain tough and survival techniques were developed to handle them. The percentage of censoring in the data affects the performance of the models by ^{1, 2}.
Nonparametric, parametric, and semiparametric survival analysis models were used to fit the censored data. In a parametric approach, different statistical distributions, including exponential, Weibull, gamma, Lindley, and loglogistic, have been suggested to handle lifetime data.
New generalisations of Lindley’s models have been developed in the past few years such as Alpha power transformed power Lindley distribution ^{3}, modified Lindley ^{4} and a new class of Lindley distribution and its properties and applications are discussed in ^{5}. The ExponentialLindley model
The key benefit of creating a new family of lifetime models is the improvement in flexibility and fit at the expense of one or more extra parameters. These new lifetime models are essential for handling failure data in a variety of sectors, including the life sciences, biological sciences, medicine, and industry.
The main objective of this work is to explore the utility of ExponentialLindley models in the presence of Type I and Type II censoring. No major work has been made to model censored survival data using ExponentialLindley (EL) distribution using different censoring schemes. In this paper typeI and typeII censoring were considered with different levels of censoring mechanisms.
The rest of the section is laid out as follows. In Section 2, the ExponentialLindley model and its graphical representation, as well as the methodology applied are presented. Section 3 presents the findings and related discussion. In section 4, ends with the main conclusion.
Lindley distribution fundamental properties with application to lifetime data was proposed by Ghitany ^{9}. Extend the Lindley model by using the concept of an exponential generator of probability distribution to create a new model ExponentialLindley was developed Balogun ^{4}. The twoparameter model was using an exponential generator (ExpG family) with an additional shape parameter (λ
The EL density function varies significantly depending on the values of shape parameters
The ExponentialLindley model is skewed and flexible, and its shape is determined by the parameters' values. The survival, hazard functions and Cumulative hazard are
Let us consider “d” to be the death among the n individuals who die at times t_{1}, t_{2}…t_{d} and that the remaining survival times of (nd) individuals t_{1}^{*}, t_{2}^{*}… t_{nd}^{*} are rightcensored. Let δ_{i} be the indicator variable that takes the value zero when survival time is censored and unity when is uncensored. The likelihood of the sample data can be obtained by using
The corresponding Loglikelihood for the equation (2.6) is given by
Using (2.1) and (2.3) in (2.6) to get the new likelihood function for the proposed model as,
The LogLikelihood function can be written as,
The nonlinear equation can be solved using Newton Raphson’s numerical methods.
The model comparisons are evaluated using Deviance (2LL), AIC (Akaike Information Criterion) and BIC (Bayesian Information Criterion) defined as
AIC = 2LL + 2k
BIC = 2LL +k (log N)
Where k is the number of parameters involved in the model and N is the sample size.
The common type of censoring occurs when the survival time is "incomplete" on the right side of the followup period. Right censorship happens when a participant leaves the study before an event happens or when the study is over before the event has taken place. In this article, TypeI and TypeII rightcensored observations were considered.
The TypeI right censored sample has the form (T_{i},
The loglikelihood is given by for EL density
In this censoring scheme, the observations are recorded until a prespecified s (s
Hence, Type II censoring data consists of the s smallest ordered observations 0
For EL density
The ExponentialLindley model is generated from the ExponentialG family of distributions and the Lindley distribution is a mixture of exponential and gamma distributions. A simulation study, was carried out the performance of the ExponentialLindley model under TypeI and TypeII censoring schemes. As a result, the exponential distribution is used to generate the random samples t_{1}, t_{2}…








100 
5% 
ExponentialLindley 
0.6045 
1.8203 



Power Lindley 
2.2017 
1.2425 
95 
99 
99 

Gamma 
0.4778 
1.3013 
101 
105 
105 

BurrXII 
2.4323 
1.4370 
111 
115 
115 

Lindley 
2.1245 
 
101 
103 
103 

Exponential 
1.6094 
 
105 
107 
107 

10% 
ExponentialLindley 
0.6147 
1.8027 




Power Lindley 
2.1957 
1.2399 
96 
100 
100 

Gamma 
0.4795 
1.2986 
101 
105 
105 

BurrXII 
2.4263 
1.4349 
112 
116 
116 

Lindley 
2.1207 
 
101 
103 
103 

Exponential 
1.6060 
 
106 
108 
108 

20% 
ExponentialLindley 
0.6615 
1.7210 




Power Lindley 
2.1595 
1.2251 
99 
103 
103 

Gamma 
0.4920 
1.2824 
104 
108 
108 

BurrXII 
2.3894 
1.4225 
115 
119 
119 

Lindley 
2.0968 
 
104 
106 
106 

Exponential 
1.5850 
 
108 
110 
110 

300 
5% 
ExponentialLindley 
0.4522 
1.922 



Power Lindley 
2.0088 
1.3397 
327 
331 
332 

Gamma 
0.4724 
1.4493 
350 
354 
355 

BurrXII 
2.2218 
1.5659 
381 
385 
386 

Lindley 
1.9549 
 
357 
359 
360 

Exponential 
1.4606 
 
373 
375 
376 

10% 
ExponentialLindley 
0.4740 
1.8710 




Power Lindley 
1.9909 
1.3300 
332 
336 
337 

Gamma 
0.4790 
1.4390 
355 
359 
360 

BurrXII 
2.2038 
1.5581 
386 
390 
391 

Lindley 
1.9436 
 
362 
364 
365 

Exponential 
1.4508 
 
377 
379 
380 

20% 
ExponentialLindley 
0.4889 
1.8370 




Power Lindley 
1.9781 
1.3232 
336 
340 
341 

Gamma 
0.4839 
1.4315 
358 
362 
363 

BurrXII 
2.1908 
1.5525 
390 
394 
395 

Lindley 
1.9354 
 
365 
367 
368 

Exponential 
1.4436 
 
380 
382 
383 

500 
5% 
ExponentialLindley 
0.4545 
1.7698 



Power Lindley 
1.8015 
1.3635 
631 
635 
636 

Gamma 
0.4978 
1.5139 
671 
675 
676 

BurrXII 
2.001 
1,6228 
726 
730 
731 

Lindley 
1.8008 
 
688 
690 
691 

Exponential 
1.3270 
 
717 
719 
720 

10% 
ExponentialLindley 
0.4626 
1.7523 




Power Lindley 
1.7961 
1.3598 
634 
638 
639 

Gamma 
0.5003 
1.5098 
674 
678 
679 

BurrXII 
1.9953 
1.6200 
729 
733 
734 

Lindley 
1.7971 
 
691 
693 
694 

Exponential 
1.3238 

720 
722 
723 

20% 
ExponentialLindley 
0.4852 
1.7027 




Power Lindley 
1.7779 
1.3478 
645 
649 
650 

Gamma 
0.5091 
1.4962 
684 
688 
689 

BurrXII 
1.9766 
1.6101 
740 
744 
745 

Lindley 
1.7843 
 
700 
702 
703 

Exponential 
1.3128 
 
728 
730 
731 








100 
5% 
ExponentialLindley 
0.6546 
1.7467 



Power Lindley 
2.1882 
1.2348 
96 
100 
100 

Gamma 
0.4821 
1.2945 
102 
106 
106 

BurrXII 
2.4203 
1.4320 
112 
116 
116 

Lindley 
2.1165 
 
102 
104 
104 

Exponential 
1.6024 
 
106 
108 
108 

10% 
ExponentialLindley 
0.6969 
1.6847 




Power Lindley 
2.1679 
1.2256 
98 
102 
102 

Gamma 
0.4891 
1.2850 
104 
108 
108 

BurrXII 
2.4002 
1.4249 
114 
118 
118 

Lindley 
2.1034 
 
104 
106 
106 

Exponential 
1.5908 
 
108 
110 
110 

20% 
ExponentialLindley 
0.7992 
1.5391 




Power Lindley 
2.0975 
1.1965 
106 
110 
110 

Gamma 
0.5158 
1.2524 
110 
114 
114 

BurrXII 
2.3275 
1.401 
120 
124 
124 

Lindley 
2.0546 
 
110 
112 
112 

Exponential 
1.5479 
 
112 
114 
114 

300 
5% 
ExponentialLindley 
0.6995 
1.5125 



Power Lindley 
1.8971 
1.2708 
364 
368 
369 

Gamma 
0.5191 
1.3792 
382 
386 
387 

BurrXII 
2.1115 
1.5148 
414 
418 
419 

Lindley 
1.8816 
 
386 
388 
389 

Exponential 
1.3969 
 
400 
402 
403 

10% 
ExponentialLindley 
0.7600 
1.4425 




Power Lindley 
1.8773 
1.2578 
372 
376 
377 

Gamma 
0.5288 
1.3658 
388 
392 
393 

BurrXII 
2.0917 
1.5053 
422 
426 
427 

Lindley 
1.8674 
 
392 
394 
395 

Exponential 
1.3846 
 
404 
406 
407 

20% 
ExponentialLindley 
0.8878 
1.3008 




Power Lindley 
1.8124 
1.2211 
396 
400 
401 

Gamma 
0.5633 
1.3231 
410 
414 
415 

BurrXII 
2.0235 
1.4742 
444 
448 
449 

Lindley 
1.8176 
 
410 
412 
413 

Exponential 
1.3415 
 
424 
426 
427 

500 
5% 
ExponentialLindley 
0.5430 
1.7043 



Power Lindley 
1.9084 
1.4480 
558 
562 
563 

Gamma 
0.4119 
1.7485 
592 
596 
597 

BurrXII 
2.1407 
1.7579 
628 
632 
633 

Lindley 
1.8721 
 
642 
644 
645 

Exponential 
1.3886 
 
672 
674 
675 

10% 
ExponentialLindley 
0.6127 
1.5912 




Power Lindley 
1.8700 
1.4201 
580 
584 
585 

Gamma 
0.4262 
1.7143 
612 
616 
617 

BurrXII 
2.1008 
1.7364 
648 
652 
653 

Lindley 
1.8492 
 
658 
660 
661 

Exponential 
1.3688 
 
688 
690 
691 

20% 
ExponentialLindley 
0.7124 
1.4268 




Power Lindley 
1.7721 
1.3616 
640 
644 
645 

Gamma 
0.4678 
1.6294 
666 
670 
671 

BurrXII 
1.9925 
1.6821 
708 
712 
713 

Lindley 
1.7834 
 
700 
702 
703 

Exponential 
1.3120 
 
728 
730 
731 
The study was carried out at the Medical Centre of the University of West Virginia, USA. The data related to 48 patients with multiple myeloma, all of whom were aged between 50 and 80 years. Out of these 48 patients, 12 (25%) had censored survival times. The survival times were recorded in months. Other details can be seen in Krall et al. (1975). The results of the analysis were presented in




ExponentialLindley 
0.0149 
10.6991 
372 
Power Lindley 
0.1824 
0.7608 
400 
Gamma 
1.0790 
21.6632 
398 
BurrXII 
0.0075 
50.9551 
444 
Lindley 
0.0823 
 
408 
Exponential 
0.0428 
 
399 
Further
The study results are presented in tables
This research article has concentrated on real and simulated (TypeI and TypeII) rightcensored data sets with different censoring percentages. The result of the simulated TypeI and TypeII rightcensored data revealed that the EL model performed better than the other models based on Deviance, AIC, and BIC values. The performance of the model improves with increase in sample size and decrease with censoring. As a result of the real data, the proposed model has a lower Deviance value than the other models. The ExponentialLindley model better performed than the other underlying models. Further work is needed for other levels of censoring and sample sizes and also on parametric regression models.