On the Product-Moments of Various Orders of the Normal Correlation Surface of Two Variates

Biometrika ◽  
1918 ◽  
Vol 12 (1/2) ◽  
pp. 86 ◽  
Author(s):  
K. Pearson ◽  
A. W. Young
Keyword(s):  
Product Moments ◽  
Normal Correlation

scholarly journals Relations for Moments of Generalized Order Statistics for Transmuted Exponential Distribution and Characterization

2021 ◽  
pp. 43-50
Author(s):  
Saman Shahbaz ◽  
Mashail Al-Sobhi ◽  
Rehan Ahmad Khan Sherwani
Keyword(s):  
Order Statistics ◽  
Exponential Distribution ◽  
Generalized Order Statistics ◽  
Product Moments ◽  
Recursive Computation ◽  
Single And Product Moments ◽  
Generalized Order

The relations for moments of generalized order statistics (gos) for transmuted exponential distribution are obtained. These include relations for single, inverse, product and ratio moments. These relations are useful in for recursive computation of moments of gos for transmuted exponential distribution. Some characterizations of the distribution, based on single and product moments of gos, are also obtained.

scholarly journals Islamic equities and COVID-19 pandemic: measuring Islamic stock indices correlation and volatility in period of crisis

2021 ◽  
Vol 29 (1) ◽  
pp. 50-66
Author(s):  
Shafiu Ibrahim Abdullahi
Keyword(s):  
Stock Market ◽  
Generalized Method Of Moments ◽  
Multivariate Garch ◽  
Content Type ◽  
Volatility Transmission ◽  
Distributed Lag ◽  
Autoregressive Distributed Lag ◽  
Stock Indices ◽  
Cointegration Tests ◽  
Normal Correlation

PurposeThe purpose of the study is to measure cross-country stock market correlation and volatility transmission during the global coronavirus disease 2019 (COVID-19) pandemic. The paper traces trajectory of Islamic equity investments in order to get insights on the behavior of the markets during the crisis.Design/methodology/approachThe paper uses generalized method of moments (GMM), autoregressive distributed lag (ARDL) and multivariate GARCH (MGARCH) models for analysis of dynamic causality, stock market cointegration, correlation and volatility transmission between Islamic stock indices.FindingsThe result of normal correlation analysis on the share indices show the markets move together. The result of ARDL cointegration test shows the markets returns are cointegrated as a group. To further make sense of the data; the indices were grouped into four different categories, then cointegration tests were conducted. The results of the analysis show that the subgroups are cointegrated except the low COVID-19 subgroup. Based on MGARCH findings, the possibility of volatility transmission between markets during the crisis is high. The market returns indices show the usual herd mentality common during the period of crisis.Originality/valueUnlike other works in this area, this paper attempt to trace the trajectory of Islamic equity investment in order to get relevant insights and arrives at appropriate ways of responding to the crisis.

Product Moments, Material Eternities

2019 ◽  
pp. 161-165
Author(s):  
Jonathan Chapman
Keyword(s):  
Product Moments

Normal correlation.

2011 ◽  
pp. 317-334
Author(s):  
G. Udny Yule
Keyword(s):  
Normal Correlation

VII.—The Correlation between Product Moments of any Order in Samples from a Normal Population

1930 ◽  
Vol 49 ◽  
pp. 78-90 ◽  
Author(s):  
John Wishart
Keyword(s):  
Normal Population ◽  
Considerable Importance ◽  
Subsequent Work ◽  
Product Moments ◽  
The Right

1. A problem of considerable importance in the theory of statistics is the determination of the accuracy with which a given sample of observations determines the characteristics of the population from which it is derived. Any parameter of this distribution can only in practice be estimated from the sample, and the degree of latitude in our choice of the right function enables considerations of suitability and efficiency of the particular moment statistic to be taken into account. As well as this, however, the probable errors of such frequency constants, or, to be more complete, the distribution of the constants in all possible samples, must be determined. These problems were formulated many years ago by Karl Pearson (1), and his important researches have stimulated and suggested much subsequent work.

scholarly journals Statistics for Ratios of Rayleigh, Rician, Nakagami-m, and Weibull Distributed Random Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Dragana Č. Pavlović ◽  
Nikola M. Sekulović ◽  
Gradimir V. Milovanović ◽  
Aleksandra S. Panajotović ◽  
Mihajlo Č. Stefanović ◽  
...  
Keyword(s):  
Random Variables ◽  
Joint Probability ◽  
Wireless Systems ◽  
Technical Literature ◽  
Product Moments ◽  
Outdoor Environments ◽  
Indoor And Outdoor Environments ◽  
Analytical Expressions ◽  
Joint Probability Density ◽  
Indoor And Outdoor

The distributions of ratios of random variables are of interest in many areas of the sciences. In this brief paper, we present the joint probability density function (PDF) and PDF of maximum of ratiosμ1=R1/r1andμ2=R2/r2for the cases whereR1,R2,r1, andr2are Rayleigh, Rician, Nakagami-m, and Weibull distributed random variables. Random variablesR1andR2, as well as random variablesr1andr2, are correlated. Ascertaining on the suitability of the Weibull distribution to describe fading in both indoor and outdoor environments, special attention is dedicated to the case of Weibull random variables. For this case, analytical expressions for the joint PDF, PDF of maximum, PDF of minimum, and product moments of arbitrary number of ratiosμi=Ri/ri,i=1,…,Lare obtained. Random variables in numerator,Ri, as well as random variables in denominator,ri, are exponentially correlated. To the best of the authors' knowledge, analytical expressions for the PDF of minimum and product moments of{μi}i=1Lare novel in the open technical literature. The proposed mathematical analysis is complemented by various numerical results. An application of presented theoretical results is illustrated with respect to performance assessment of wireless systems.

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