Understanding Gamma Distributed RV: Finding Shape and Scale Parameters

In summary, When writing a gamma distributed RV, the shape and scale parameters must be known. If given the equation of the gamma distributed RV, the scale and shape parameters can be found mathematically.
  • #1
EngWiPy
1,368
61
Hello,

When writting a gamma distributed RV we need to know the shape and scale parameters. How to find the value of these parameters?

Thanks in advance
 
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  • #2
What do you mean by find these parameters? Do you wish to estimate the parameters of a gamma distribution from some data?
 
  • #3
Focus said:
What do you mean by find these parameters? Do you wish to estimate the parameters of a gamma distribution from some data?

No, I meant if we are given the equation of the gamma distributed RV, how to find these parameters from this equation? Mathematically:
[tex]\gamma = \frac{\|\mathbf{h}\|^2P}{N_0}[/tex]
where [tex]\mathbf{h}[/tex] is a column vector of Nakagami-m distributed RVs. Then how to find the scale and shape parameters from this equation?
 

What is a Gamma distributed random variable?

A Gamma distributed random variable is a continuous probability distribution that is used to model the time it takes for a certain number of events to occur. It is often used in fields such as engineering, finance, and biology to analyze waiting times and failure rates.

How is a Gamma distributed random variable different from other distributions?

The main difference between a Gamma distributed random variable and other distributions is its ability to model waiting times or time until a certain number of events occur. It is also unique in that it has two parameters, shape and scale, that can be adjusted to fit a wide range of data.

What types of data can be modeled using a Gamma distributed random variable?

A Gamma distributed random variable is often used to model real-world phenomena such as waiting times, failure rates, and inter-arrival times. It can also be used to model insurance claims, stock returns, and rainfall amounts.

What are the parameters of a Gamma distributed random variable?

The parameters of a Gamma distributed random variable are shape and scale. The shape parameter, denoted by alpha (α), determines the shape of the distribution curve and can take on any positive real value. The scale parameter, denoted by beta (β), affects the spread of the distribution and can also take on any positive real value.

How is a Gamma distributed random variable calculated?

The probability density function (PDF) for a Gamma distributed random variable is given by f(x) = (x^(α-1) * e^(-x/β)) / (β^α * Γ(α)), where x is the random variable, α is the shape parameter, β is the scale parameter, and Γ(α) is the gamma function. It can also be calculated using statistical software or by looking up values in a Gamma distribution table.

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