Normdf: Difference between revisions
Jump to navigation
Jump to search
imported>Jeremy (Importing text file) |
imported>Bob |
||
| (4 intermediate revisions by one other user not shown) | |||
| Line 1: | Line 1: | ||
===Purpose=== | ===Purpose=== | ||
Normal / Gaussian distribution. | Normal / Gaussian distribution. | ||
===Synopsis=== | ===Synopsis=== | ||
:prob = normdf(function,x,a,b) | :prob = normdf(function,x,a,b) | ||
===Description=== | ===Description=== | ||
Estimates cumulative distribution function (cumulative, cdf), probability density function (density, pdf), quantile (inverse of cdf), or random numbers for a Normal distribution. | 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. | 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. | ||
* 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' ]. | ::<math>f(x)= \frac {1} {b \left ( 2 \pi \right ) ^ {1/2}} \exp \left [ \frac {- \left ( x -a \right )^2} {2b^2} \right ]</math> | ||
* x = matrix in which the sample data is stored, in the interval (-inf,inf). | |||
====Inputs==== | |||
* a = mode/location parameter (real). | |||
* b = scale parameter (real and positive). | * '''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''': 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=== | ||
====Cumulative | |||
>> prob = normdf('c',[1.9600 2.5758]) | ====Cumulative==== | ||
<pre>>> prob = normdf('c',[1.9600 2.5758]) | |||
ans = | ans = | ||
0.9750 0.9950 | 0.9750 0.9950 | ||
>> x = -5:.1:5; | >> x = -5:.1:5; | ||
>> plot(x,normdf('c',x,0,1)), vline([ 0 ; normdf('q',[0.975; 0.995],0,1)]) | >> plot(x,normdf('c',x,0,1)), vline([ 0 ; normdf('q',[0.975; 0.995],0,1)]) | ||
====Density | </pre> | ||
====Density==== | |||
<pre> | |||
>> prob = normdf('d',[1.9600 2.5758],0,1) | >> prob = normdf('d',[1.9600 2.5758],0,1) | ||
ans = | ans = | ||
| Line 29: | Line 50: | ||
>> x = -5:.1:5; | >> x = -5:.1:5; | ||
>> plot(x,normdf('d',x,0,1)), vline([0; normdf('q',[0.975; 0.995],0,1)]) | >> plot(x,normdf('d',x,0,1)), vline([0; normdf('q',[0.975; 0.995],0,1)]) | ||
====Quantile | </pre> | ||
>> | ====Quantile==== | ||
<pre> | |||
>> prob = normdf('q',[.975 .995],0,1) | |||
ans = | ans = | ||
1.9600 2.5758 | 1.9600 2.5758 | ||
====Random | </pre> | ||
====Random==== | |||
<pre> | |||
>> prob = normdf('r',[4 1],0,1) | >> prob = normdf('r',[4 1],0,1) | ||
ans = | ans = | ||
| Line 40: | Line 65: | ||
0.1253 | 0.1253 | ||
0.2877 | 0.2877 | ||
</pre> | |||
===See Also=== | ===See Also=== | ||
[[ | |||
[[betadf]], [[cauchydf]], [[chidf]], [[expdf]], [[gammadf]], [[gumbeldf]], [[laplacedf]], [[logisdf]], [[lognormdf]], [[paretodf]], [[raydf]], [[triangledf]], [[unifdf]], [[weibulldf]] | |||
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