|
|
 |
| |
|
|
|
On Translations, Contractions, and Dilations of Order Statistics and Record Values from the Extended Erlang–Truncated Exponential Distribution |
|
|
|
PP: 647-657 |
|
|
doi:10.18576/jsap/150319
|
|
|
|
Author(s) |
|
|
|
Imtiyaz A. Shah,
|
|
|
|
Abstract |
|
|
| In this study, a new continuous distribution called the Erlang-truncated exponential (ETE) distribution is introduced and studied. The Erlang-truncated exponential (ETE) distribution is modified and the new lifetime distribution is called the extended Erlang- truncated exponential (EETE) distribution. Some statistical and reliability properties of the new distribution are given and the method of moment generating function estimate was proposed for estimating the model parameters. The usefulness and flexibility of the EETE distribution was illustrated with an uncensored data set and its fit was compared with that of the ETE and three other three-parameter distributions. Order statistics and record values play an important role in statistical inference, reliability analysis, and extreme value studies. In this paper, we investigate the properties of order statistics and record values arising from the Erlang–truncated exponential distribution. Particular attention is given to the effects of linear transformations, namely translations, contractions, and dilations. Explicit expressions for the probability density functions and distribution functions of order statistics and record values are obtained, and several important distributional properties are derived. The behavior of these statistics under the considered transformations is examined in detail. The results provide useful insights into the structural properties of the Erlang–truncated exponential distribution and may have applications in reliability theory, survival analysis, and life-testing experiments. |
|
|
|
|
|
|
|
