# $$\text{GammaVariate}$$¶

You can use the $$\text{GammaVariate}$$ function to calculate one or more random variates in a gamma distribution.

You can use the \gammav backslash command to insert this function.

The following variants of this function are available:

• $$\text{real } \text{GammaVariate} \left ( \text{<k>} \right )$$

• $$\text{real } \text{GammaVariate} \left ( \text{<k>}, \text{<}\theta\text{>} \right )$$

• $$\text{real matrix } \text{GammaVariate} \left ( \text{<number rows>}, \text{<number columns>}, \text{<k>} \right )$$

• $$\text{real matrix } \text{GammaVariate} \left ( \text{<number rows>}, \text{<number columns>}, \text{<k>}, \text{<}\theta\text{>} \right )$$

Where $$k$$, and $$\theta$$ are scalar values representing the shape shape term and the scale term respectively. Note that these functions are defined over the range $$k > 0$$ and $$\theta > 0$$ and will generate an error or return NaN for values for which the function is not defined.

The three and four parameter versions, which includes $$\text{<number rows>}$$ and $$\text{<number columns>}$$ fields, returns an real matrix returning random deviates. The one and two parameter versions return a single value.

This function calculates random variates using the method described in [3].

The gamma distribution can be viewed as the sum of $$k$$ identical and independent exponential distributions with rate $$\frac{1}{\theta}$$. The exponential distribution is therefore the special case of the gamma distribution with $$k = 1$$. Similarly, the gamma distribution is also equivalent to the Erlang distribution when $$k$$ is an integer value.

The gamma distribution is identical to the chi-squared distribution with $$v$$ degrees of freedom when $$k = \frac{1}{2} v$$ and $$\theta = 2$$.

Figure 144 shows the basic use of the $$\text{GammaVariate}$$ function.

Figure 144 Example Use Of The GammaVariate Function