Normdf: Difference between revisions
imported>Jeremy No edit summary |
imported>Bob |
||
| Line 13: | Line 13: | ||
This distribution is used for many data types including physical attributes and sums of quantities. It is a symmetric distribution and the variance can be smaller, equal, or larger than the mean. | This distribution is used for many data types including physical attributes and sums of quantities. It is a symmetric distribution and the variance can be smaller, equal, or larger than the mean. | ||
::<math>f(x)= \frac {1} {b \left ( 2 \pi \right ) ^ {1/2}} \exp \left [ \frac {- \left ( x -a \right )^2} {2b^2} \right ]</math> | |||
====Inputs==== | ====Inputs==== | ||
| Line 29: | Line 31: | ||
'''Note''': If inputs (x, a, and b) are not equal in size, the function will attempt to resize all inputs to the largest input using the RESIZE function. | '''Note''': If inputs (x, a, and b) are not equal in size, the function will attempt to resize all inputs to the largest input using the RESIZE function. | ||
'''Note''': Functions will typically allow input values outside of the acceptable range to be passed but such values will return NaN in the results. | '''Note''': Functions will typically allow input values outside of the acceptable range to be passed but such values will return NaN in the results. | ||
===Examples=== | ===Examples=== | ||
Latest revision as of 08:41, 10 October 2008
Purpose
Normal / Gaussian distribution.
Synopsis
- prob = normdf(function,x,a,b)
Description
Estimates cumulative distribution function (cumulative, cdf), probability density function (density, pdf), quantile (inverse of cdf), or random numbers for a Normal distribution.
This distribution is used for many data types including physical attributes and sums of quantities. It is a symmetric distribution and the variance can be smaller, equal, or larger than the mean.
![{\displaystyle f(x)={\frac {1}{b\left(2\pi \right)^{1/2}}}\exp \left[{\frac {-\left(x-a\right)^{2}}{2b^{2}}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0e69273c0a55d75b342fd7569664e81a3d8e2cc6)
Inputs
- function = [ {'cumulative'} | 'density' | 'quantile' | 'random' ], defines the functionality to be used. Note that the function recognizes the first letter of each string so that the string could be: [ 'c' | 'd' | 'q' | 'r' ].
- x = matrix in which the sample data is stored, in the interval (-inf,inf).
- for function=quantile - matrix with values in the interval (0,1).
- for function=random - vector indicating the size of the random matrix to create.
- a = mode/location parameter (real).
- b = scale parameter (real and positive).
Note: If inputs (x, a, and b) are not equal in size, the function will attempt to resize all inputs to the largest input using the RESIZE function.
Note: Functions will typically allow input values outside of the acceptable range to be passed but such values will return NaN in the results.
Examples
Cumulative
>> prob = normdf('c',[1.9600 2.5758])
ans =
0.9750 0.9950
>> x = -5:.1:5;
>> plot(x,normdf('c',x,0,1)), vline([ 0 ; normdf('q',[0.975; 0.995],0,1)])
Density
>> prob = normdf('d',[1.9600 2.5758],0,1)
ans =
0.0584 0.0145
>> x = -5:.1:5;
>> plot(x,normdf('d',x,0,1)), vline([0; normdf('q',[0.975; 0.995],0,1)])
Quantile
>> prob = normdf('q',[.975 .995],0,1)
ans =
1.9600 2.5758
Random
>> prob = normdf('r',[4 1],0,1)
ans =
-0.4326
-1.6656
0.1253
0.2877
See Also
betadf, cauchydf, chidf, expdf, gammadf, gumbeldf, laplacedf, logisdf, lognormdf, paretodf, raydf, triangledf, unifdf, weibulldf