الفهرس 
INTRODUCTIONOnly 14 pages are availabe for public view
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Abstract
The progressive Type-II right censoring scheme is of great importance in life-testing experiments
as it allows the experimenter to remove units from the experiment before its end,
thus resulting in a saving in cost as well as experimental time.
In this thesis, the progressively Type-II right censored samples for some useful distributions
including the logistic, half-logistic and log-logistic distributions are considered. First,
some new recurrence relations satisfied by the single and product moments of progressively
censored sample are established for the underlying distributions. Some well known recurrence
relations in literature are deduced as special cases from our results. The BLUE(s)
and MLE(s) of the scale(location-scale) parameter(s), of the considered distributions are
derived and discussed. To show the usefulness of our results in the thesis, Monte Carlo
simulations are carried out. The performance of the proposed estimates is investigated by
calculating the mean squared errors (MSEs) for the obtained estimates. Finally, we conclude
with the following points:
In the first chapter of the thesis, a method of censoring known as progressive Type-II
censoring along with some special cases (order statistics, Type-I and Type-II censoring) are
presented. Notations of the moments of order statistics and progressive Type-II censoring
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are given. Applications to inference, including BLUE and MLE are presented for any scale
and location-scale family of distributions. BLUPs are also presented for any scale and
location-scale family of distributions.
In the second chapter of the thesis, we establish several recurrence relations for the
single and product moments of progressively Type-II right censored order statistics from a
logistic distribution. The use of these relations in a systematic manner allows us to compute
all the means, variances and covariances of progressively Type-II right censored order
statistics from the logistic distribution for all sample sizes n, effective sample sizes m, and
all progressive censoring schemes (R1; ¢ ¢ ¢ ;Rm): The results established here generalize the
corresponding results for the usual order statistics due to Shah (1966, 1970). These moments
are then utilized to derive BLUEs of the location and scale parameters of the logistic
distribution. A comparison of these estimators with the MLEs is then made. The BLUPs of
censored failure times are briefly discussed. Finally, an illustrative example is presented.
In the third chapter of the thesis, we establish several recurrence relations for the single
and product moments of progressively Type-II right censored order statistics from a halflogistic
distribution. The use of these relations in a systematic recursive manner would
enable one to compute all the means, variances and covariances of progressively Type-II
right censored order statistics from the half-logistic distribution for all sample sizes n, effective
sample sizes m, and all progressive censoring schemes (R1; ¢ ¢ ¢ ;Rm). The results
established here generalize the corresponding results for the usual order statistics due to
Balakrishnan (1985). These moments are then utilized to derive BLUEs of the scale and
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location-scale parameters of the half-logistic distribution. A comparison of these estimators
with the MLEs is then made. The BLUPs of censored failure times are then briefly
discussed. Finally, two numerical examples are presented to illustrate all the inferential
methods developed here.
In the fourth chapter of the thesis, we establish several recurrence relations for the single
and product moments of progressively Type-II right censored order statistics from a
log-logistic distribution. The use of these relations in a systematic recursive manner would
enable the computation of all the means, variances and covariances of progressively Type-
II right censored order statistics from the log-logistic distribution for all sample sizes n,
effective sample sizes m, and all progressive censoring schemes (R1; ¢ ¢ ¢ ;Rm): The results
established here generalize the corresponding results for the usual order statistics due to
Balakrishnan and Malik (1987) and Balakrishnan et al. (1987). The moments so determined
are then utilized to derive BLUEs for the scale and location-scale log-logistic distributions.
A comparison of these estimates with the MLEs is made through Monte Carlo
simulation. The BLUPs of progressively censored failure times are then briefly discussed.
Finally, a numerical example is presented to illustrate all the methods of inference developed
here.
Finally, in the last chapter of the thesis, we conclude the work that have been done.
Then, we suggest some ideas that could lead to future research.