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The continuous type of variable in continuous probability distribution consists of the probability density function, called the pdf. Because in the continuous probability distribution the variable is not countable, it is measured with respect to the density.
A normal distribution in the continuous probability distribution generally falls in between the range of -∞ to +∞. This continuous probability distribution has the parameter as µ (called the mean) and σ2 (called the variance). The probability density function (pdf) of this continuous probability distribution is being given by the following:
f(x;µ, σ)= (1/ σ π
) exp(-0.5 (x-µ)2/ σ2).This kind of continuous probability distribution has an important role in statistical theory for several reasons.
The distributions, like the Binomial distribution, Poisson distribution and Hyper Geometric distribution, are approximated by using the continuous probability distribution.
This type of continuous probability distribution is very much applicable in the Statistical Quality Control (SQC).
This type of continuous probability distribution is used in the study of large sample theory, when the normality is involved. The study of the sample statistics is done with the help of the curves of this type of continuous probability distribution.
The theory on which the significance tests (like the t-test or the F test) are based use assumptions that are assumed on the parent population, which belongs to this type of continuous probability distribution.
A continuous probability distribution called the gamma distribution generally falls in the range of 0 to ∞. This type of continuous probability distribution has the parameter ‘d>0’. The probability density function (pdf) of the continuous probability distribution is given by the following:
f(x)= exp(-x) xd-1/
This continuous probability distribution has a property called the additive property, which tells that the sum of the independent variables of this continuous probability distribution is equal to the variable of this continuous probability distribution.
A continuous probability distribution called beta distribution of the first kind has the range which ranges between 0 and 1. The parameters of this type of continuous probability distribution is µ>0 and v>0. The probability density function (pdf) of this type of continuous probability distribution is given by the following:
f(x)= (1/B(µ,v)) xµ-1 (1-x)v-1
A continuous probability distribution called the beta distribution of the second kind falls in the range of 0 to ∞. This type of continuous probability distribution has the parameters namely µ>0 and v>0.The probability density function (pdf) of this continuous probability distribution is given by the following:
f(x)= (1/B(µ,v)) xµ-1 (1+x)v+µ
The continuous probability distribution called the Weibul distribution falls in the range of µ to ∞. This type of continuous probability distribution consists of three parameters, namely c(>0), α(>0) and µ. The probability density function (pdf) in continuous probability distribution is given by the following:
f(x;c,α,µ) = (c (x-µ/α)c-1)/ α exp (-(x-µ/α)c)
A logistic distribution is a continuous probability distribution with the parameter α and β. This type of continuous probability distribution is used widely as a growth function in population and other demographic studies. This type of continuous probability distribution is considered as the mixture of the extreme values of the distributions.
A Cauchy distribution is a continuous probability distribution with the parameter ‘l’ > 0 and ‘µ’. This type of continuous probability distribution has the range of -∞ to +∞. The continuous probability distribution is given by the following:
f(x)= l/π(l2+(x-µ)2)
