On the bounds of the expected nearest neighbor distance

In this paper, we give some contributions for special distributions having unbounded support    for which we derive upper and lower bounds on the expected nearest neighbor distance of the extreme value (Gumbel) distribution as typical

Some Features of Joint Confidence Regions for the Parameters of the Inverse Weibull Distribution

In this paper, we will study the joint confidence regions for the parameters of inverse Weibull distribution in the point of view of record values. One of the applications of the joint confidence regions of the parameters is to find confidence bounds for the functions of the parameters. Joint confidence regions for the parameters of extreme value distribution are also discussed. In this way we will discus some numerical examples with real data set and simulated data, to illustrate the proposed method. A simulation study is performed to compare the proposed joint confidence regions. Keywords: The joint confidence regions, confidence bounds; inverse Weibull distribution, extreme value distribution

An Investigation of Inference of the Generalized Extreme Value Distribution Based on Record

In this article, the maximum likelihood and Bayes estimates of the generalized extreme value distribution based on record values are investigated. The asymptotic confidence intervals as well as bootstrap confidence are proposed. The Bayes estimators cannot be obtained in closed form so the MCMC method are used to calculate Bayes estimates as well as the credible intervals. A numerical example is provided to illustrate the proposed estimation methods developed here. Keywords: Generalized extreme value distribution, Record values, Maximum likelihood estimation, Bayesian estimation

A Study of The Saudi Stock Market Using Some Statistical Models

The objective of this paper is to estimate the diversification effects/benefits of an investment in a portfolio consisting of the South African Industrial (J520) and the Financial (J580) Indices using the Generalised Pareto Distributions (GPDs) with an extreme value Gumbel copula. The GPD is used as the marginal distribution to both assets to better characterize the extreme risk of returns in both Indices tails. The extreme value Gumbel copula captures the dependence structure (co-movement) of the financial assets in the portfolio. The Akaike information criterion (AIC) and Bayesian information criterion (BIC) goodness of fit tests and the scatterplots indicate that the upper tail of the gains (the larger gains) risk and the losses tail (the larger losses) are best captured using the extreme value Gumbel copula. Monte Carlo simulation of an equally weighted portfolio of the two Indices is used to estimate the portfolio risk. The univariate marginal risks and the portfolio risks are used to calculate the diversification effects/benefits. The results show that there are benefits in diversification since the riskiness of the portfolio is less than the sum of the risk of the two financial assets. This implies that VaR, although not additive theoretically, is sub-additive in this practical situation. This property of sub-additivity represents the benefits of diversification for a portfolio. The implication is that investors investing in individual risky assets can benefit from constructing such a portfolio to reduce extreme risk. Due to high dependence and contagion between developed markets/Global markets, this is useful information for local and international investors seeking a portfolio which includes developing countries market Indices, such as South African assets, which are less correlated with other Global markets, thereby reducing the risk of contagion

Financial market index prediction using machine learning

The present work aims to tackle the crucial objective of forecasting values for a range of financial market indices in order to maximize income while minimizing potential losses. This study utilizes a comparative analysis approach to examine the performance of artificial neural networks (ANNs) and decision tree models in predicting stock market movements in Saudi Arabia (KSA). The analysis is conducted using a daily database. The predictive models included in this study are constructed using historical stock market data, which encompasses the time period from January 1, 2013, to October 4, 2023. The primary objective of these models is to generate accurate projections specifically for the Tadawul Daily Index. The main objective of this study is to evaluate and contrast the effectiveness of artificial neural network (ANN) and decision tree models in predicting the performance of the stock market in Saudi Arabia. The analysis demonstrates that the decision tree model has a somewhat lower predictive capability when compared to the artificial neural network (ANN) model. The present study utilizes statistical metrics, namely root-mean-squared error (RMSE) and mean absolute error (MAE), to assess and quantify the accuracy of predictions. Moreover, a thorough examination is undertaken, encompassing a range of relevant statistical indicators, and visually representing the data series using graphical means. The utilization of a diverse methodology serves to augment knowledge and facilitate a comprehensive grasp of the intrinsic daily patterns observed in the Tadawul Daily Index. The objective is to enhance the understanding and examination of the complexities of the stock market, so empowering investors and financial analysts to make educated choices that match with their strategic goals and risk management methods. The studys findings provide significant contributions to the field of financial market prediction, specifically in the Kingdom of Saudi Arabia

Using Statistical Model to Study the Daily Closing Price Index in the Kingdom of Saudi Arabia (KSA)

Classification in statistics is usually used to solve the problems of identifying to which set of categories, such as subpopulations, new observation belongs, based on a training set of data containing information (or instances) whose category membership is known. The article aims to use the Gaussian Mixture Model to model the daily closing price index over the period of 1/1/2013 to 16/8/2020 in the Kingdom of Saudi Arabia. The daily closing price index over the period declined, which might be the effect of corona virus, and the mean of the study period is about 7866.965. The closing price is the last regular deal that took place during the continuous trading period. If there are no transactions on the stock during the day, the closing price is the previous day’s closing price. The closing auction period comes after the continuous trading period (from 3 : 00 PM to 3 : 10 PM), during which investors can enter by buying and selling the stocks at this period. The experimental results show that the best mixture model is E (equal variance) with three components according to the BIC criterion. The expectation-maximization (EM) algorithm converged in 2 repetitions. The data source is from Tadawul KSA

Forecasting and classification of new cases of COVID 19 before vaccination using decision trees and Gaussian mixture model

Regarding the pandemic taking place in the world from the spread of the Coronavirus pandemic and viral mutations, the need has arisen to analyze the epidemic data in terms of numbers of infected and deaths, different geographical regions, and the dynamics of the spread of the virus. In China, the total number of reported infections is 224,659 on June 11, 2022. In this paper, the Gaussian Mixture Model and the decision tree method were used to classify and predict new cases of the virus. Although we focus mainly on the Chinese case, the model is general and adapted to any context without loss of validity of the qualitative results. The Chi-Squared (χ2) Automatic Interaction Detection (CHAID) was applied in creating the decision tree structure, the data has been classified into five classes, according to the BIC criterion. The best mixture model is the E (Equal variance) with five components. The considered data sets of the world health organization (WHO) were used from January 5, 2020, to 12, November 2021. We provide numerical results based on the Chinese case

Predication and Photon Statistics of a Three-Level System in the Photon Added Negative Binomial Distribution

Statistical and artificial neural network models are applied to forecast the quantum scheme of a three-level atomic system (3LAS) and field, initially following a photon added negative binomial distribution (PANBD). The Mandel parameter is used to detect the photon statistics of a radiation field. Explicit forms of the PANBD are given. The prediction of the Mandel parameter, atomic probability of the 3LAS in the upper state, and von Neumann entropy are obtained using time series and artificial neural network methods. The influence of probability success photons and the number of added photons to the NBD are examined. The total density matrix is used to compute and analyze the time evolution of the initial photonic negative binomial probability distribution that governs the 3LAS–field photon entanglement behavior. It is shown that the statistical quantities are strongly affected by probability success photons and the number of added photons to the NBD. Also, the prediction of quantum entropy is achieved by the time series and neural network

Generalized Type-I Hybrid Censoring Scheme in Estimation Competing Risks Chen Lifetime Populations

Different types of censoring scheme are investigated; however, statistical inference on censoring scheme which can save the ideal test time and the minimum number of failures is needed. The generalized type-I hybrid censoring scheme (GHCS) solves this problem. Competing the risk models under the GHCS when time to failure has Chen lifetime distribution (CD) is adopted in this research with consideration of only two cases of failure. Partially step-stress accelerated life tests (ALTs) are applied to obtain enough failure times in a small period to achieve a highly reliable product. The problem of parameter estimation under maximum likelihood (ML) and Bayes methods is discussed. The asymptotic confidence interval as well as the Bayes credible interval is constructed. The validity of theoretical results is assessed and compared through simulation study. Finally, brief comments are reported to describe the behaviour of the estimation results