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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

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Exponential-modified discrete Lindley distribution.

Mehmet Yilmaz¹, Monireh Hameldarbandi², Sibel Acik Kemaloglu¹

¹Department of Statistics, Faculty of Science, Ankara University, 06100 Tandogan, Ankara Turkey.

|October 13, 2016

Summary

This summary is machine-generated.

This study introduces a new lifetime distribution for series systems with a random number of components. The zero truncated modified discrete Lindley distribution is analyzed, and its parameters are estimated using various statistical methods.

Keywords:

Discrete Lindley distribution EM-algorithm Exponential- modified Maximum likelihood estimation Method of moments Modified discrete Lindley distribution

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Area of Science:

Reliability Engineering
Probability Theory
Statistical Modeling

Background:

Series systems are crucial in engineering, and their reliability depends on component lifetimes.
Component redundancy and the number of components (M) significantly impact system performance.
Existing lifetime distributions may not adequately capture the complexities of systems with a random number of components.

Purpose of the Study:

To introduce and analyze a novel lifetime distribution for series systems with a stochastically independent M-component structure.
To investigate the properties of this new distribution, specifically the zero truncated modified discrete Lindley distribution.
To estimate the parameters of the proposed lifetime distribution using established statistical techniques.

Main Methods:

A series system model with M stochastically independent components was considered.
A new distribution, the zero truncated modified discrete Lindley distribution, was derived by transforming the original parameter.
Parameter estimation was performed using the method of moments, maximum likelihood estimation, and the expectation-maximization (EM) algorithm.

Main Results:

The properties of the lifetime distribution for the series system were examined under the specified conditions.
The newly introduced zero truncated modified discrete Lindley distribution was characterized.
Successful parameter estimation was achieved through the application of moments, maximum likelihood, and EM-algorithm.

Conclusions:

The study successfully introduced and analyzed a new lifetime distribution for series systems with a random number of components.
The proposed distribution, based on the zero truncated modified discrete Lindley distribution, offers a valuable tool for reliability analysis.
The employed estimation methods provide robust approaches for parameter determination in this novel distribution.