A Comparison between Some Bayesian Estimation Methods for
Parameter Exponential Distribution by Using Data Type II Censoring

Abstract. Due to the importance of exponential distribution, especially in the modeling a nd
analysis of various data in several fields in mathematics and statistics, inclu d in g th e a pplied
field (experiments) and the pure field (theories). Some tests do not provide sufficient
information on the trial data, so they are called “censored data”. The a im o f this paper is to
compare some Bayesian estimation methods for the exponential dist ribution of parameters
using data type II censoring. We provided an estimate of the scale parameter (ESP) for the
exponential distribution under data the control of type II by using the proposed Bayesian
method and maximum probability. We a lso compared these methods using Mean square erro r
(MSE). This study was conducted using simulation with different parameter values (?) a nd
different sample sizes (n = 10, 20, 50, 100). The calculation results showed that the best
method of estimation is the proposed Bayesian method (BAY2), which uses the distribution o f
Chi-Square (n) in the previous information.

The exponential distribution is the most important mathematical models, which has very many
applications in several life’s areas in general and in mathematics in particular for both pure and
applied where used in the modelling and analysis of data, in previous years, many researchers have
reached to several results using this distribution see [1],[2] and [3].Usually, when the researcher
performs some tests, the researcher may lack the ability to monitor and identify all the elements that
have been selected on the basis of which the success of the experiment depends on its failure, the most
important reasons: Some of them are related to the temporal factor of the experiment and some of
them are related to constraints (such as financial cost and others) which negatively effect on the
results. Therefore, when these effects are directly low with the number of failure observed state s, the
controlled experience of failure is better, more effective, and achieves less time and effort than the
time-controlled experiment. After that, the researchers identified the experiment, which was controlled
by failure, as surveillance type II. In this type of experiment, the test is terminated as soon as the
number failures that pre-determined (r) is the number of units (n) that is tested. The researchers [4],
[5], [6], [7],[8] and [9]presented the definition of predictive distribution in the life’s areas and reached
several results in this area. The methods of estimating Bayesian are studied in the classical exponential
distribution (see [11]) and reached to the best methods of estimating through this distribution. In 2007,
the researcher [12] also studied the Bayes estimation of the exponential distribution under double
control of type II.Then the researchers used a set of previous distributions to estimate the parameter by
exponential distribution. See [10]. The aim of this research is to compare some of the theoretical
estimation methods for the exponential distribution of the parameters by using data type control II. We
provided an estimate of the measurement parameter (ESP) of the exponential distribution under the
data, and control of the second type that is using the proposed Bayes method and maximum
probability. We also compared these methods using MSE (Mean Square Error).