Gamma Distribution

A gamma distribution is a continuous probability distribution that is commonly used to model positive-valued variables. It is characterized by its shape and scale parameters. The shape parameter determines the shape of the distribution, while the scale parameter influences the spread. The gamma distribution is typically skewed and has a shape that can be varied by adjusting its parameters.

The gamma distribution is commonly used in areas such as reliability analysis, queuing theory, and modelling waiting times.

Gamma Probability Distribution

In MatDeck, the gammadist function is used calculate the cumulative distributions function for the gamma distribution. The function only requires 3 arguments and can handle several different data types. We can see this below in the gammadist function which is called inside the curve2d function.

The first argument is the value or values for which you would like to calculate the gamma CDF, it can be a single number or it can be a vector which contains multiple different value which the gamma function would be applied to. The second argument is the mean/ average of the population, this can be directly obtained from data using the average function. The final argument is the standard deviation of the data, just like the mean/average you can directly calculate the standard deviation

Here is an in-depth explanation of all the Gamma Probability Distribution functions:

• gamma-dist function
• gamma-dens function

Inverse Gamma Probability Distribution

The inverse gamma distribution is the mathematical operation that calculates the value corresponding to a specified probability under a given gamma distribution. It provides the inverse mapping of the cumulative distribution function (CDF) of the gamma distribution.

Gamma Distributions in Python

All MD functions are available to be used in Python via MD Python. This includes all Mathematical and Statistical. The MD Python bindings allow Python users to natively call and use MatDeck functions in their work, this allows them to access C++ speed with the simple syntax of Python. It gives them unparalleled access to the MatDeck library, without them needing any experience to excel.

Uses of the Gamma Distribution

The Gamma Distribution is used in various fields when dealing with continuous variables that represent the waiting time until a certain number of events occur. It is preferred over other distributions in certain scenarios because:

• It is suitable for modelling continuous data representing waiting times or durations.
• It is applicable when events occur independently and follow a gamma-shaped pattern.
• It assumes memorylessness, making it suitable for independent events.
• It has a flexible parameterization with shape and scale parameters, allowing for a wide range of distributions.
• It is analytically tractable for calculating probabilities and statistics.
• It is often used for modelling time-to-failure, queueing systems, and insurance claim amounts.

However, the Gamma Distribution may not be appropriate if events do not occur independently or if the data does not follow a gamma-shaped pattern. In such cases, alternative distributions may be more suitable based on the specific data characteristics and research question.