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
Domain: mathworld.wolfram.com
| DC.Title | Pearson System |
| DC.Creator | Weisstein, Eric W. |
| DC.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... |
| DC.Subject | 62E |
| DC.Rights | Copyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement. |
| DC.Format | text/html |
| DC.Identifier | https://mathworld.wolfram.com/PearsonSystem.html |
| DC.Language | en |
| DC.Publisher | Wolfram Research, Inc. |
| DC.Relation.IsPartOf | https://mathworld.wolfram.com/ |
| DC.Type | Text |
| og:image | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_PearsonSystem.png |
| og:type | website |
| twitter:card | summary_large_image |
| twitter:image:src | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_PearsonSystem.png |
| None | ie=edge |
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