Coursework 1
Question 1
1- a) description of the exponential family of distri preciselyions.
The exponential function family of distributions is a general class of one- contention distributions that can be nonstop or discrete and share a certain trunk:
Where T(x), h(x), ?(?), and A(?) are known functions.
The value ? is called the parameter of the family.
Also
* , and cannot be unique i.e. can be multiplied by a constant and T can be divided by the same constant.
* The range of in is not allowed to = 0 and not be dependent on.
* Cannot be seen negatively in the simple form of.
Note
The Binomial, Normal, Gamma, Poisson and Multinomial statistical models are some of the nearly commonly used statistical models and they are members of the Exponential family of distributions.
b) Definition of the canonical form of a distribution.
The canonical form is a simplified form of the general form of the exponential family of distributions. The in the form can be multiplied by some(prenominal) nonzero constant, however is multiplied by its inverse making the canonical form non-unique with.
c) Definition of nuisance parameter.
A nuisance parameter is used to identify a parameter that is needed but not being investigated or of interest immediately i.e. the faulting parameter in a Linear Regression Model or in the normal distribution.
2- The following probability parsimoniousness function belongs to the Bernoulli distribution:
Using the above probability niggardness function it can be shown that the Bernoulli distribution belongs to the exponential family of distribution i.e.
* The above probability density function can be expressed as follows:
Where and
* The above can also be expressed as:
* By taking...If you want to get a full essay, order it on our website: Orderessay
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