Quantile in Julia

In Statistics field, when we do the hypothesis testing, we have to get the quantile of a specific distribution so we go to find its value in the table. This method is out of dated, we should embrace the modern technology and exploit it.

Julia is a powerful programming language designed for technical computing. As it own saying that Julia: A fresh approach to technical computing.

Today, we are going to teach you how to get the quantile of a specific distribution in short time with only line of code.

Preparation

1. You should have Julia installed on your device.
2. Install the package Distribution

    using Pkg
    Pkg.add("Distribution")
   

3. Import the package Distribution

    using Distribution
   

Common Distribution

First of all, we should get the Distribution object.

For example, if we need to use Standard Normal Distribution,

N = Normal(0,1)

then you get it.

Common Distribution you may use.

# N(μ,σ):	the Normal distribution
Normal(μ,σ)
# χ²(n):	the ChiSquare distribution
Chisq(n)
# t(n):		the T distribution
TDist(n)

Calculate Quantile

Now, we discuss how to get the Quantile in Julia.

It is so easy as you only need to call function quantile to approach your goal.

quantile(d::UnivariateDistribution, q::Real)

Above, it is the basic grammar of the function quantile.

Maybe it seem abstract to you, so let see some simple example to help you understand it.

1. $u_{0.975}$: The $0.975$ quantile of Standard Normal Distribution $N(0,1)$

    U=Normal()
    quantile(U,0.975)
    # return 1.9599639845400576
   

2. $t_{0.95}(15)$ :The $0.95$ quantile of $t(15)$: T Distribution with $15$ freedom

   T₍₁₅₎=TDist(15)
   quantile(T₍₁₅₎,0.95)
   # return 1.7530503556925727
   

3. $\chi_{0.025}^2(24)$： The $0.025$ quantile of $\chi^2(24)$ : ChiSquare Distribution with $24$ freedom

    χ²₍₂₄₎=Chisq(24)
    quantile(χ²₍₂₄₎,0.025)
    # return 12.401150217444433
   

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