Continuous Distribution
Continuous Distribution
.Standard Normal Distribution
Pdf: e^(-x^2/2)/√2π Here N(0,1) which Mean is 0 and variance is 1 And similarly we have
.Normal Distribution
Pdf: e^((-(x-μ)^2)⁄(2σ^2)) /σ√2π Here N(µ,σ^2) where mean is µ and variance is σ^2
These distribution is mostly used in health and motor insurance and these distribution use for those events which are most likely to follow probabilistic pattern in the future.
If the data is more and there is more uncertainty then the distribution of the estimated parameter approves normal.
These distributions are used to help, predict and adjust for a wide range of financial goal by optimising financial decision making by applying and graphically mapping the data into distribution.
.Gamma Distribution
Pdf: λ^α/Γα x^(α-1) e^(-λx) Here mean is α/λ and variance is α/λ^2
“α” changes the shape of the graph of the PDF and “λ” changes the X-scale.
It represents the uncertainty of the Poisson process.
When we put α=1 then it becomes the exponential distribution.
It has Pdf= λe^(-λx)
And the exponential distribution has the “Memoryless” property.
P(X>x+n|X>n)= P(X>x)
.Beta Distribution
Pdf: Γ(α+β)/Γ(α)Γ(β) x^(α-1) 〖(1-x)〗^(β-1) Where mean is α/(α+β) and variance is αβ/((α+β)^2 (α+β+1))
It describes uncertainty distribution for the probability of binomial process given observed data.
In beta distribution there is a wide range of shapes and over many finite range of graphs.
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