Continuous probability distribution is that type of distribution that deals with continuous type of data or random variables. The continuous random variables deal with different kinds of continuous probability distribution.
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There are different continuous probability distributions.
A normal distribution is a continuous probability distribution with parameters µ ( called the mean) and s2 (called the variance) that have a range of -8 to +8. Its continuous probability distribution is given by the following:
f(x;µ, s)= (1/ s p) exp(-0.5 (x-µ)2/ s2).
This type of continuous probability distribution plays a crucial role in statistical theory for several reasons. Most of the distributions, like binomial, poisson and hyper geometric distributions are approximated with the help of this continuous probability distribution.
This continuous probability distribution finds a large number of applications in Statistical Quality Control.
This type of continuous probability distribution is used widely in the study of large sample theory where normality is involved. Sample statistics can be best studied with the help of the curves of this type of continuous probability distribution.
The overall theory of significance tests (like t test, F test, etc.) are entirely based upon the fundamental assumption that the parent population belongs to this type of continuous probability distribution.
Even if the variable is not following this type of continuous probability distribution, then it can be transformed into this type of continuous probability distribution.
A gamma distribution is a continuous probability distribution with the parameter ‘d>0’that has a range of 0 to 8. Its continuous probability distribution is given by the following:
f(x)= exp(-x) xd-1/
This type of continuous probability distribution has a property called the additive property. This property states that the sum of the independent variates of this continuous probability distribution is equal to the variate of this continuous probability distribution.
A beta distribution of the first kind is a continuous probability distribution with the parameters µ>0 and v>0 that has the range of 0 to 1. Its continuous probability distribution is given by the following:
f(x)= (1/B(µ,v)) xµ-1 (1-x)v-1
A beta distribution of the second kind is a continuous probability distribution with the parameters µ>0 and v>0 that has the range of 0 to 8. Its continuous probability distribution is given by the following:
f(x)= (1/B(µ,v)) xµ-1 (1+x)v+µ
An exponential distribution is a continuous probability distribution with the parameter ‘c’ >0 that has the range of 0 to 8. Its continuous probability distribution is given by the following:
f(x,c)= c exp(-cx)
A standard laplace or double exponential distribution is a continuous probability distribution with no parameter. The reason that there is no parameter in this type of continuous probability distribution is because this continuous probability distribution is standardized in nature. Thus, this continuous probability distribution does not have any parameters. Its continuous probability distribution is given by the following:
f(x)= 0.5 exp (- )
A weibul distribution is a continuous probability distribution with three parameters c(>0), a(>0) and µ that has the range of µ to 8. Its continuous probability distribution is given by the following:
f(x;c,a,µ) = (c (x-µ/a)c-1)/ a exp (-(x-µ/a)c)
A logistic distribution is a continuous probability distribution with parameter a and ß. 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 to be the mixture of the extreme values of the distributions.
A Cauchy distribution is a continuous probability distribution with parameter ‘l’ > 0 and ‘µ.’ This type of continuous probability distribution has the range of -8 to +8. The continuous probability distribution is given by the following:
f(x)= l/p(l2+(x-µ)2)
This type of continuous probability distribution follows the additive property as stated above. The type of continuous probability distribution plays a role in providing counter examples.
Showing posts with label Continuous Probability Distribution. Show all posts
Showing posts with label Continuous Probability Distribution. Show all posts
Thursday, December 17, 2009
Monday, June 15, 2009
Continuous Probability Distribution
The continuous probability distribution is basically a kind of distribution that is based on the continuous type of random variables. The continuous type of random variable deals with the continuous probability distribution.
Statistics Solutions can assist with continuous probability distribution analysis for your dissertation, thesis or research. Contact Statistics Solutions today for a free 30-minute consultation.
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)
Statistics Solutions can assist with continuous probability distribution analysis for your dissertation, thesis or research. Contact Statistics Solutions today for a free 30-minute consultation.
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)
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