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B. Stat. – 201 |
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| Aim of this course | |||||||||||||||||||
| This course is designed to afford basic concept and the application of transformation, sampling distribution and order statistics. | |||||||||||||||||||
| Objective of this course | |||||||||||||||||||
| ⇒ | Transfer one variable to another variable by different method of transformation. | ||||||||||||||||||
| ⇒ | Depict the role of sampling distributions in inferential statistics. | ||||||||||||||||||
| ⇒ | Demonstrate general strategies for problems about order statistics | ||||||||||||||||||
| ⇒ | Explore the application area of order statistics in real life as well as statistical theory. | ||||||||||||||||||
| Learning outcome of this course | |||||||||||||||||||
| At the end of the course the students will be able to | |||||||||||||||||||
| ⇒ | apply different methods of transformation in various distributions. | ||||||||||||||||||
| ⇒ | estimate the sampling distribution of mean, variance, correlation and regression coefficients. | ||||||||||||||||||
| ⇒ | the shape of sampling distribution to interpret the nature of statistical data. | ||||||||||||||||||
| ⇒ | establish the interrelationship in t, F and chi-square distribution. | ||||||||||||||||||
| ⇒ | derive the distribution function of the smallest, largest and rth order statistic | ||||||||||||||||||
| ⇒ | construct confidence interval for quantities and distribution free tolerance interval. | ||||||||||||||||||
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| Course Contents | ||||||||||||||||||
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Transformation of Variables: Introduction, Distribution of function of random variable(s), Probability integral transformation, Transformation of variables-using Jacobian, Distribution function and moment generating function techniques, Problem on transformation of variables related to Binomial, Poisson, Uniform, Normal, Exponential, Gamma, Beta, Weibull and Extreme value distributions, Delta methods for finding mean and variance of function of random variable(s).
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Sampling Distributions: Introduction, Meaning of parent and sampling distributions, Methods of deriving sampling distribution, Fisher’s lemma, c2, t and F distributions with their properties and applications, Distribution of sample mean, variance, skewness, kurtosis, proportion and difference between two sample proportions, Distribution of Regression and correlation coefficients for null case.
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Distribution of Order Statistics: Introduction, Joint and marginal distributions of order statistics, Distribution of functions of order statistics, Illustrations from different parent distributions, Expected values and moments of order statistics, Applications.
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| Main Books Recommended: | ||||||||||||||||||
| 1) | Hogg, R. and A.T. Craig (2002): Introduction to Mathematical Statistics, 8th ed., Pearson Education Asia. | |||||||||||||||||
| 2) | Marx, M. L., & R. J. Larsen (2006). Introduction to mathematical statistics and its applications. Pearson/Prentice Hall. | |||||||||||||||||
| References: | ||||||||||||||||||
| 3) | Bartoszynski, R., & M. Niewiadomska-Bugaj (2007). Probability and statistical inference. John Wiley & Sons. | |||||||||||||||||
| 4) | Brunk, H. D., & T. Teichmann (2009). An introduction to mathematical statistics. Physics Today, 13(11), 50-52. [Bijma, Tucker] | |||||||||||||||||
| 5) | David, H.A. (1980): Order Statistics, 2nd ed., Wiley, N.Y. | |||||||||||||||||
| 6) | Forbes, C., M. Evans, N. Hastings, & B. Peacock (2011). Statistical distributions. John Wiley & Sons. | |||||||||||||||||
| 7) | Johnson, N. L., A. W. Kemp, & S. Kotz (2005). Univariate discrete distributions. John Wiley & Sons. | |||||||||||||||||
| 8) | Kendall, M.G. and A. Stuart (2004): Advanced Theory of Statistics, 14th ed., Edward Arnold, N.Y. [Volume01, Volume02, Volume02, 3rd ed] | |||||||||||||||||
| 9) | Kotz, S., N. Balakrishnan and N. L. Johnson (2000): Continuous Multivariate Distributions, Vol. 1, Models and Applications, 2nd ed., Wiley, N.Y. | |||||||||||||||||
| 10) | Mood, A.M., F. A. Graybill and D.C. Boes (2013). Introduction to the theory of Statistics. 11th ed., McGraw–Hill, N.Y. | |||||||||||||||||