nbinstat
Negative binomial mean and variance
Description
Examples
Calculate Mean and Variance for Negative Binomial Distribution
Generate vectors of values for the number of successes and probability of success in each trial.
P = 0.1:0.2:0.9; R = 1:5;
For each pair of elements in P
and R
, calculate the mean and variance for the corresponding negative binomial distribution.
[M,V] = nbinstat(R,P)
M = 1×5
9.0000 4.6667 3.0000 1.7143 0.5556
V = 1×5
90.0000 15.5556 6.0000 2.4490 0.6173
Each pair of elements in the vectors M
and V
contains the mean and variance for the negative binomial distributions corresponding to the pairs of elements at the same positions in P
and R
.
Input Arguments
R
— Number of successes
positive scalar value | array of positive scalar values
Number of successes, specified as a positive scalar value or an array of positive
scalar values. The elements of R
can be noninteger values. If both
R
and P
are arrays, they must be the same
size. If either R
or P
is a scalar, then
nbinstat
expands the scalar argument into a constant array of
the same size as the other argument.
Example: [3 1 7]
Data Types: single
| double
P
— Probability of success
positive scalar value | array of positive scalar values
Probability of success in a single trial, specified as a positive scalar value or an
array of positive scalar values. The elements of P
must be between
0 and 1. If both P
and R
are arrays, they must
be the same size. If either P
or R
is a
scalar, then nbinstat
expands the scalar argument into a
constant array of the same size as the other argument.
Example: [0.5 0.25 0.75]
Data Types: single
| double
Output Arguments
M
— Mean
numeric scalar | array of numeric scalars
Mean for the negative binomial distribution, returned as a numeric scalar or an
array of numeric scalars. M
is the same size as
R
and P
. Each element in
M
is the mean of the negative binomial distribution specified by
the corresponding elements in R
and P
. For
more information, see Mean.
Data Types: single
| double
V
— Variance
numeric scalar | array of numeric scalars
Variance for the negative binomial distribution, returned as a numeric scalar or an
array of numeric scalars. V
is the same size as
R
and P
. Each element in
V
is the variance of the negative binomial distribution specified
by the corresponding elements in R
and P
. For
more information, see Variance.
Data Types: single
| double
More About
Mean
The mean m of the negative binomial distribution with r successes and probability p of success in each trial is given by the formula
Variance
The variance v of the negative binomial distribution with r successes and probability p of success in each trial is given by the formula
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
Version History
Introduced before R2006a
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