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Journal of Statistics and Computer Science

Journal of Statistics and Computer Science

Frequency :Bi-Annual

ISSN :2583-5068

Peer Reviewed Journal

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Table of Content :-Journal of Statistics and Computer Science , Vol:1, Issue:2, Year:2022

Formal Analysis of Penalty Functions in Constrained Optimization with Genetic Algorithms

BY :   Wim Hordijk
Journal of Statistics and Computer Science , Year:2022, Vol.1 (2), PP.111-118
Received:25 September 2022 | Revised:08 November 2022 | Accepted :08 November 2022 | Publication:15 December 2022
Doi No.:https://doi.org/10.47509/JSCS.2022.v01i02.01

It is well known that using a penalty function can significantly improve the search performance of a genetic algorithm (GA) on constrained optimization problems. However, although it is intuitively clear, there is very little theory for why and how this actually works. Here, a formal investigation into this phenomenon is presented in terms of a schema analysis and a Walsh function analysis. This explicitly elucidates two particular mechanisms by which a penalty function can improve GA search performance.

Keywords: Machine learning; Schema analysis; Walsh function analysis

Wim Hordijk (2022). Formal Analysis of Penalty Functions in Constrained Optimization with Genetic Algorithms. Journal of Statistics and Computer Science. 1(2), 111-118.

TWO-WAY ANOVA: INFERENCES ABOUT AN INTERACTION, BASED ON A ROBUST HETEROSCEDASTIC MEASURE OF EFFECT SIZE, WHEN THERE IS A COVARIATE

BY :   Rand R. Wilcox
Journal of Statistics and Computer Science , Year:2022, Vol.1 (2), PP.119-134
Received:28 September 2022 | Revised:12 November 2022 | Accepted :16 November 2022 | Publication:15 December 2022
Doi No.:https://doi.org/10.47509/JSCS.2022.v01i02.02

Recently, there have been advances on characterizing an interaction in a two-way ANOVA design in a manner that takes into account simultaneously some robust mea- sure of location and some robust measure of dispersion. These methods allow het-eroscedasticity. The first goal in this paper is to suggest an analog of one of these measures of e ect size when there is a covariate. Extant results related to the pro-posed method suggest how to make inferences about the proposed measure of e ect size, but even for moderately small sample size, they proved to be unsatisfactory. The second goal here is to suggest a method for dealing with this issue.

keywords: robust e ect size, heteroscedasticity, quantile regression estimator


Approximating General Discrete Stochastic Processes by Markov Chains

BY :   András Faragó
Journal of Statistics and Computer Science , Year:2022, Vol.1 (2), PP.135-145
Received:10 October 2022 | Revised:30 October 2022 | Accepted :18 November 2022 | Publication:15 December 2022
Doi No.:https://doi.org/10.47509/JSCS.2022.v01i02.03

Many modeling tasks in stochastic systems and networks lead to discrete stochastic processes. In lucky cases, the stochastic process is a Markov chain, for which well elaborated mathematical machinery is available. Occasionally, however, one may en-counter more complex situations when the Markov property does not hold. This is the case, for example, when the system exhibits long-range dependencies. Another example is when the system depends on some random initial condition, which gives rise to di erent behavior, such as di erent transition probabilities, yielding a mixture of Markov chains, rather than a single one. Yet another situation is when the current state of the system may be correlated with its future evolution, it does not exclusively depend only on the past. In these and other non-Markovian instances signi cantly fewer general methods are available to serve the analysis. We present an approach to (partially) overcome this diculty. Speci cally, we consider the approximation of general discrete stochastic processes by Markov chains. We prove that this approach allows the application of many pieces of Markov chain based analysis methods and algorithms to the more general case, thus usefully extending the application domain of a number of well-known methods and algorithms.

Keywords: Discrete stochastic process, Markov chain, approximation.

András Faragó (2022). Approximating General Discrete Stochastic Processes by Markov Chains. Journal of Statistics and Computer Science. 1(2), 135-145.

Estimation of Stress Strength Reliability for New Generalized Pareto Distribution using Advanced Sampling Methods

BY :   C. J. Rehana and K. Jayakumar
Journal of Statistics and Computer Science , Year:2022, Vol.1 (2), PP.147-158
Received:20 October 2022 | Revised:10 November 2022 | Accepted :22 November 2022 | Publication:15 December 2022
Doi No.:https://doi.org/10.47509/JSCS.2022.v01i02.04

In reliability theory, the issue with stress strength estimation has many applications. The R = P(X < Y) stress-strength reliability is applied to describe the survival rate of a component which has X as stress applied and Y as the strength of the system. In the present article, we investigate the R estimation in case where two independent random variables X and Y are used each having New Generalized Pareto distribution based on some advanced sampling methods. The suggested sampling methods are "simple random sampling, ranked set sampling and percentile ranked set sampling". We propose the maximum likelihood estimator of R, when observations for two random variables are chosen using different sampling approaches. Output of proposed estimators for R based on percentile ranked set sampling and ranked set sampling with the simple random sampling equivalent is compared through the simulation study. Estimator efficiencies are measured using ratio of mean square errors. For illustrations, real data set is also analyzed.

Keywords: Maximum Likelihood, New generalized Pareto distribution, Percentile ranked set sampling, Ranked set sampling, Stress strength reliability.

MSC 2020 subject classification: 62D99, 62F99.

C.J. Rekhana & K. Jayakumar (2022). Estimation of Stress Strength Reliability for New Generalized Pareto Distribution using Advanced Sampling Methods. Journal of Statistics and Computer Science. 1(2), 147-158.

Combinatorial Matrices from Certain Balanced Incomplete Block Designs

BY :   Shyam Saurabh
Journal of Statistics and Computer Science , Year:2022, Vol.1 (2), PP.159-164
Received:02 November 2022 | Revised:28 November 2022 | Accepted :05 December 2022 | Publication:15 December 2022
Doi No.:https://doi.org/10.47509/JSCS.2022.v01i02.05

Some combinatorial matrices are obtained from affine resolvable and near resolvable designs. These matrices are used in the construction of group divisible designs and Latin square type designs which are important families of two associate classes partially balanced incomplete block designs.

MSC: 62K10; 05B05

Keywords: Balanced incomplete block design; Difference matrices; Generalised Weighing matrices; Near resolvable designs

Shyam Saurabh (2022). Combinatorial Matrices from Certain Balanced Incomplete Block Designs. Journal of Statistics and Computer Science. 1(2), 159-164.

Improved Control Charts to Monitor Changes in the Location Parameter

BY :   Gadre M. P. and Rattihalli R. N.
Journal of Statistics and Computer Science , Year:2022, Vol.1 (2), PP.165-187
Received:02 November 2022 | Revised:28 November 2022 | Accepted :05 December 2022 | Publication:15 December 2022
Doi No.:https://doi.org/10.47509/JSCS.2022.v01i02.06

For univariate / multivariate processes, we propose an ‘Improved Control Chart to monitor the Location parameter’ (ICC-L). Looking at the comparative study based on illustrative examples considered, it is observed that under the ATS criterion, ICC-L performs uniformly better than the related charts and it is also better than the ‘Modified Control Chart with Warning Limits’ (MCCWL) to detect shifts in the location parameter. ICC-L may be used to monitor the production process.


Keywords: Control Limits, Warning Limits, Average Run Length, Average Time to Signal

Gadre M.P., & Rattihalli R.N. (2022). Improved Control Charts to Monitor Changes in the Location Parameter. Journal of Statistics and Computer Science. 1(2), 165-187.

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