Admission to Ph.D in Statistics course will be based on the marks obtained in the entrance test held by the concerned University or college. Both objective and subjective type questions are asked in this entrance exam so as to test the knowledge of the applicants. Only postgraduates with adequate score can apply for this exam.

Institutes offering Ph.D in Statistics course are Meerut College, Gulbarga University, Kurukshetra University, Rajasthan Vidyapeeth University, Gauhati University etc.

Entrance exam for Ph.D in Statistics

Ph. D in Statistics entrance test consists of two parts that is objective part and subjective part. Only multiple choice questions will be asked in objective part. Candidates can choose their answers from the given options. But in subjective part, candidates need to answer in long sentences and steps. As there are only subjective type questions, more time have to be devoted for this section than objective part.

Kurukshetra University Ph.D in Statistics entrance test, University of Hyderabad Ph.D in Statistics Entrance Test and University of Calcutta Ph.D in Statistics Entrance Test are some of the popular entrance exams for Ph.D in Statistics. Syllabus of Ph.D in Statistics entrance test consists of:

Part I

• Basics of queues
• Chi-square test
• Completely Randomized Design
• Correlation and Regression
• F-test
• Large sample tests
• Latin Square Design
• Linear trend and seasonal variations
• Markov chain
• Markov Process
• Measures of Fertility and Mortality
• Methods of finding BFS for transportation problems
• Probability
• Probability Distribution
• Properties of good estimators
• Random Sampling and Stratified Sampling
• Randomized Blocks Design
• Simple against simple
• Simplex method
• Testing of hypothesis
• T-test

Part II

Unit I

• Bhattacharya Bounds
• Borel-contelli Lemma
• Concept of likelihood function
• Cramer-Rao inequality
• Rao-Black well theorem
• Minimum mean square estimation
• Properties of a good estimator
• Tchebycheff’s and Kolmogorov’s inequalities
• Various modes of convergence

Unit II

• Geometric, Binomial, Poisson, Exponential, Beta, Normal and Gamma distributions
• Chi-square distribution
• F-distribution
• Sampling distributions
• Simple tests based on t, f, Chi-square and normal variate z
• Student-t distribution

Unit III

• Construction and analysis of completely randomized, randomized blocks and Latin-square designs
• Factorial experiment with each factor at two levels
• Optimum allocation
• PPS sampling with replacement and without replacement sampling
• Probability sampling
• Proportional allocation
• Stratified sampling
• Symmetrical factorials

Unit IV

• Distribution of sample mean vector and sample dispersion matrix
• Estimation of the mean vector and covariance matrix
• Hotteling’s T square and Mahalanobis-D square Statistic
• Marginal and Conditional distribution
• Maximum likelihood estimator of the parameters of multivariate normal distribution
• Multivariate normal distribution
• Principal components and Canonical correlation in the population

Colleges offering Ph.D in Statistics

• Indian Institute of Technology, Uttar Pradesh
• Meerut College, Uttar Pradesh
• Kurukshetra University, Haryana
• Maharshi Dayanand University, Haryana
• University of Delhi, New Delhi
• Panjab University, Chandigarh
• North Eastern Hill University, Meghalaya
• University of Calcutta, West Bengal
• Gauhati University, Assam
• Bhavnagar University, Gujarat
• Sardar Patel University, Gujarat
• Banasthali University, Rajasthan
• Mohanlal Sukhadia University, Rajasthan
• N.I.M.S. University, Rajasthan
• Rajasthan Vidyapeeth University, Rajasthan
• University of Rajasthan, Rajasthan
• North Maharashtra University, Maharashtra
• Sant Gadge Baba Amravati University, Maharashtra
• University of Mumbai, Maharashtra
• University of Pune, Maharashtra
• Gulbarga University, Karnataka
• Mangalore University, Karnataka
• Osmania University, Andhra Pradesh
• Sri Krishnadevaraya University, Andhra Pradesh
• University of Hyderabad, Andhra Pradesh
• Cochin University of Science and Technology, Kerala
• Government College, Kerala
• Nehru Arts and Science College, Kerala
• Nirmala College, Kerala
• C.B.M College of Arts and Science, Tamil Nadu

Top institutes which offer Ph.D in Statistics are Indian Institute of Technology, University of Hyderabad, University of Pune and Osmania University.