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Title: Pearson System -- from Wolfram MathWorld

Open Graph Title: Pearson System -- from Wolfram MathWorld

X Title: Pearson System -- from Wolfram MathWorld

Description: A system of equation types obtained by generalizing the differential equation for the normal distribution (dy)/(dx)=(y(m-x))/a, (1) which has solution y=Ce^((2m-x)x/(2a)), (2) to (dy)/(dx)=(y(m-x))/(a+bx+cx^2), (3) which has solution (4) Let c_1, c_2 be the roots of a+bx+cx^2. Then the possible types of curves are 0. b=c=0, a>0. E.g., normal distribution. I. b^2/4ac<0, c_1<=x<=c_2. E.g., beta distribution. II. b^2/4ac=0, c<0, -c_1<=x<=c_1 where...

Open Graph Description: A system of equation types obtained by generalizing the differential equation for the normal distribution (dy)/(dx)=(y(m-x))/a, (1) which has solution y=Ce^((2m-x)x/(2a)), (2) to (dy)/(dx)=(y(m-x))/(a+bx+cx^2), (3) which has solution (4) Let c_1, c_2 be the roots of a+bx+cx^2. Then the possible types of curves are 0. b=c=0, a>0. E.g., normal distribution. I. b^2/4ac<0, c_1<=x<=c_2. E.g., beta distribution. II. b^2/4ac=0, c<0, -c_1<=x<=c_1 where...

X Description: A system of equation types obtained by generalizing the differential equation for the normal distribution (dy)/(dx)=(y(m-x))/a, (1) which has solution y=Ce^((2m-x)x/(2a)), (2) to (dy)/(dx)=(y(m-x))/(a+bx+cx^2), (3) which has solution (4) Let c_1, c_2 be the roots of a+bx+cx^2. Then the possible types of curves are 0. b=c=0, a>0. E.g., normal distribution. I. b^2/4ac<0, c_1<=x<=c_2. E.g., beta distribution. II. b^2/4ac=0, c<0, -c_1<=x<=c_1 where...

Opengraph URL: https://mathworld.wolfram.com/PearsonSystem.html

X: @WolframResearch

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Domain: mathworld.wolfram.com

DC.TitlePearson System
DC.CreatorWeisstein, Eric W.
DC.DescriptionA system of equation types obtained by generalizing the differential equation for the normal distribution (dy)/(dx)=(y(m-x))/a, (1) which has solution y=Ce^((2m-x)x/(2a)), (2) to (dy)/(dx)=(y(m-x))/(a+bx+cx^2), (3) which has solution (4) Let c_1, c_2 be the roots of a+bx+cx^2. Then the possible types of curves are 0. b=c=0, a>0. E.g., normal distribution. I. b^2/4ac<0, c_1<=x<=c_2. E.g., beta distribution. II. b^2/4ac=0, c<0, -c_1<=x<=c_1 where...
DC.Subject62E
DC.RightsCopyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement.
DC.Formattext/html
DC.Identifierhttps://mathworld.wolfram.com/PearsonSystem.html
DC.Languageen
DC.PublisherWolfram Research, Inc.
DC.Relation.IsPartOfhttps://mathworld.wolfram.com/
DC.TypeText
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og:typewebsite
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normal distributionhttps://mathworld.wolfram.com/NormalDistribution.html
normal distributionhttps://mathworld.wolfram.com/NormalDistribution.html
beta distributionhttps://mathworld.wolfram.com/BetaDistribution.html
gamma distributionhttps://mathworld.wolfram.com/GammaDistribution.html
beta prime distributionhttps://mathworld.wolfram.com/BetaPrimeDistribution.html
Student's t-distributionhttps://mathworld.wolfram.com/Studentst-Distribution.html
modehttps://mathworld.wolfram.com/Mode.html
momenthttps://mathworld.wolfram.com/Moment.html
momentshttps://mathworld.wolfram.com/Moment.html
7https://mathworld.wolfram.com/PearsonSystem.html#eqn7
8https://mathworld.wolfram.com/PearsonSystem.html#eqn8
11https://mathworld.wolfram.com/PearsonSystem.html#eqn11
13https://mathworld.wolfram.com/PearsonSystem.html#eqn13
skewnesshttps://mathworld.wolfram.com/Skewness.html
kurtosis excesshttps://mathworld.wolfram.com/KurtosisExcess.html
bivariate normal distribution https://www.wolframalpha.com/input/?i=bivariate+normal+distribution
beta distribution https://www.wolframalpha.com/input/?i=beta+distribution
continuous distributions https://www.wolframalpha.com/input/?i=continuous+distributions
Mathematics of Statistics, Pt. 2, 2nd ed.http://www.amazon.com/exec/obidos/ASIN/B0007HR7SY/ref=nosim/ericstreasuretro
Pearson Systemhttps://www.wolframalpha.com/input/?i=pearson+system
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