Probability Distributions

Paper Code: 
STT-123
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 

This course lays the foundation of probability distributions and their application which forms the basis of Statistical Inference.

 

15.00
Unit I: 
Unit I

Bernoulli distribution, Binomial distribution (compound and truncated also), Poisson distribution (compound and truncated also) - moments ,moments generating function ,cummulant generating function ,characteristics functions,recurrence relations,properties,fitting of distributions.

15.00
Unit II: 
Unit II

Geometric distribution, Negative Binomial distribution, Hyper-geometric distributions, Power Series distribution- moments, moment generating function, cummulant generating functions, characteristics function , recurrence relations ,properties, fitting of distributions.

 

15.00
Unit III: 
Unit III

Rectangular distribution, Normal distribution (truncated also), Exponential distribution, Lognormal distribution, multinomial of binomial and poisson- moments, moment generating function,cummulant generating function , characteristics functions, recurrence relations,properties, fitting of distributions

15.00
Unit IV: 
Unit IV

Triangular distribution, Gamma distribution(one and two parameter) , Beta distribution( I kind and II kind) cauchy distribution(truncated also), laplace distributions, pearson's distribution(type I,IV & VI)

15.00
Unit V: 
Unit V

chi-square ,t and F distributios(central and non central) and their applications, large sample test. Fisher's Z distributions and their applications. Order statistics : their distributions and properties ; joint and marginal distributions of order statistics , sampling distributions of range and median of univariate population.

Essential Readings: 

Books Recommended/Reference Books

 

1. Goon, Gupta & Das Gupta. (1991): Outline of Statistical Theory. Vol. I, World Press.

2. Hogg, R.V. and Craig, A.T.(1971): Introduction to Mathematical Statistics, McMillan.

3. Johnson, S. and Kotz. (1972): Distribution in Statistics, Vol.I, II. And III, Houghton and Muffin.

4. Kendall, M.G. and Stuart. (1996): An Advanced Theory of Statistics, Vol. I,II. Charls Griffin.

5. Mood,A.M., Graybill, F.A. and Boes, D.C.(1974): Introduction to the Theory of Statistics, McGraw Hill.

6. Mukhopadhyay, P. (1996): Mathematical Statistics, New Central Book Agency (P) Ltd.

7. Rohatgi, V.K. (1984): An Introduction to Probability Theory and Mathematical Statistics, Wiley Eastern.

Academic Year: 
2018-2019
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