Paper IV of the Indian Statistical Service written examination is Statistics-Iv, and this page takes its syllabus one line at a time. Each line is reproduced as it is prescribed, then pointed at the page on this site that teaches it, with the depth stated rather than implied.
Statistics-IV (Descriptive) — 200 marks, 3 hrs.
Examination Notice No. 07/2026-IES/ISS, dated 11.02.2026 — Appendix-I, Scheme of Examination, and Section-II, Standard and SyllabiYou answer two of the seven sections. The notification states: “In Statistics-IV, there will be SEVEN Sections in the paper. Candidates have to choose any TWO Sections out of them. All Sections will carry equal marks.” So the tally below counts the whole paper; in the hall you need two sections, and the sensible choice is the pair whose rows are greenest for you.
12 syllabus lines: 3 taught in depth, 3 at exam level, 6 not here yet.
| Syllabus line, as prescribed | Where it is taught here | Depth |
|---|---|---|
| Definition and scope of operations research; phases; models and their solutions; decision-making under uncertainty and risk; different criteria; sensitivity analysis | Operations Research Unit 1 — Introduction & LPP Formulation | brief |
| Dynamic programming and its application to linear programming problems | nothing on this site teaches it | not here |
| Two-person games, pure and mixed strategies; existence and uniqueness of the value in zero-sum games; solutions of 2×2, 2×m and m×n games | Optimization Techniques Unit 4 — Game Theory | deep |
| Inventory problems; the EOQ formula of Harris, its sensitivity analysis and extensions with quantity discounts and shortages; multi-item inventory subject to constraints; models with random demand; P and Q systems | nothing on this site teaches it | not here |
| Queuing models and effectiveness measures; steady-state M/M/1 and M/M/c with queue-length and waiting-time distributions; M/G/1 and the Pollaczek–Khinchine result | UGC NET Unit IX — Stochastic Processes | brief |
| Sequencing and scheduling; 2-machine n-job and 3-machine n-job problems; branch and bound for the travelling salesman problem | Optimization Techniques Unit 3 — Sequencing Problem Optimization Techniques Unit 2 — Assignment Problem | deep |
| Replacement problems — block and age replacement policies | nothing on this site teaches it | not here |
| PERT and CPM; probability of project completion | Optimization Techniques Unit 5 — Network Scheduling (CPM & PERT) | deep |
| Reliability concepts and measures; components and systems; coherent systems and their reliability | nothing on this site teaches it | not here |
| Life distributions, reliability function, hazard rate; exponential, Weibull and gamma life distributions; bivariate exponential; estimation and tests in these models | Advanced Actuarial Statistics Unit 1 — Future Lifetime & Mortality Laws Continuous Distributions Unit 2 — Exponential Distribution | brief |
| Notions of ageing — IFR, IFRA, NBU, DMRL and NBUE classes and their duals; loss of memory property of the exponential | nothing on this site teaches it | not here |
| Reliability estimation from censored life tests and tests with replacement; stress–strength reliability and its estimation | nothing on this site teaches it | not here |
8 syllabus lines: 4 taught in depth, 3 at exam level, 1 not here yet.
| Syllabus line, as prescribed | Where it is taught here | Depth |
|---|---|---|
| Sources of demographic data — census, registration, ad-hoc surveys, hospital records; demographic profiles of the Indian census | Applied Statistics Unit 4 — Vital Statistics | deep |
| Complete life table and its main features; uses of a life table | Applied Statistics Unit 5 — Life Tables, Fertility & Population Growth | deep |
| Makeham's and Gompertz's curves; national life tables; UN model life tables; abridged life tables | Advanced Actuarial Statistics Unit 1 — Future Lifetime & Mortality Laws Actuarial Statistics Unit 3 — Survival Distribution & Life Tables | brief |
| Stable and stationary populations | Applied Statistics Unit 5 — Life Tables, Fertility & Population Growth | brief |
| Measurement of fertility — crude birth rate, general fertility rate, age-specific birth rate, total fertility rate, gross and net reproduction rates | Applied Statistics Unit 5 — Life Tables, Fertility & Population Growth | deep |
| Measurement of mortality — crude death rate, standardized death rates, age-specific death rates, infant mortality rate, death rate by cause | Applied Statistics Unit 4 — Vital Statistics | deep |
| Internal migration and its measurement; migration models; international migration; net migration | nothing on this site teaches it | not here |
| Inter-censal and post-censal estimates; projection methods including logistic curve fitting; the decennial census in India | Applied Statistics II Unit 1 — Growth Curves | brief |
9 syllabus lines: 5 taught in depth, 3 at exam level, 1 not here yet.
| Syllabus line, as prescribed | Where it is taught here | Depth |
|---|---|---|
| Time, order and random censoring; likelihood in these cases; exponential, gamma, Weibull, lognormal, Pareto and linear failure rate distributions and inference for them | Clinical Trials Unit 4 — Reporting and Analysis Continuous Distributions Unit 2 — Exponential Distribution | brief |
| Life tables, failure rate, mean residual life and their elementary classes and properties | Actuarial Statistics Unit 3 — Survival Distribution & Life Tables | brief |
| Estimation of the survival function — actuarial estimator, Kaplan–Meier estimator; estimation under IFR or DFR; tests of exponentiality against non-parametric classes; total time on test | Clinical Trials Unit 4 — Reporting and Analysis | deep |
| Two-sample problem — Gehan test, log-rank test; semi-parametric regression for the failure rate; rank test for the regression coefficient | Clinical Trials Unit 4 — Reporting and Analysis | deep |
| Competing risk model; parametric and non-parametric inference for it | nothing on this site teaches it | not here |
| Introduction to clinical trials: need and ethics; bias and random error; conduct of trials; Phase I to IV; multicentre trials | Clinical Trials Unit 1 — Introduction to Clinical Trials | deep |
| Data management — data definitions, case report forms, database design, data collection systems for good clinical practice | Clinical Trials Unit 1 — Introduction to Clinical Trials | brief |
| Design of clinical trials: parallel versus cross-over, cross-sectional versus longitudinal, factorial designs; objectives and endpoints; Phase I, II and III designs with sequential stopping | Clinical Trials Unit 3 — Design of Clinical Trials Clinical Trials Unit 2 — Determination of Sample Size | deep |
| Reporting and analysis — categorical outcomes from Phase I to III trials; analysis of survival data | Clinical Trials Unit 4 — Reporting and Analysis | deep |
8 syllabus lines: 6 taught in depth, 0 at exam level, 2 not here yet.
| Syllabus line, as prescribed | Where it is taught here | Depth |
|---|---|---|
| Quality of a product; need for quality control; basic concepts of process control, process capability and product control | Statistical Quality Control Unit 1 — Introduction to SQC | deep |
| General theory of control charts; causes of variation; control limits; sub-grouping; summary of out-of-control criteria | Statistical Quality Control Unit 1 — Introduction to SQC | deep |
| Charts for attributes — p, np, c and u charts | Statistical Quality Control Unit 3 — Control Charts for Attributes | deep |
| Charts for variables — X-bar and R, X-bar and s charts | Statistical Quality Control Unit 2 — Control Charts for Variables | deep |
| Process capability and process optimization | Statistical Quality Control Unit 2 — Control Charts for Variables | deep |
| OC and ARL of control charts; control by gauging; moving average and exponentially weighted moving average charts; Cu-Sum charts with V-masks and decision intervals; economic design of the X-bar chart | nothing on this site teaches it | not here |
| Acceptance sampling plans for attributes — single and double sampling plans and their properties | Statistical Quality Control Unit 4 — Acceptance Sampling for Attributes Statistical Quality Control Unit 5 — Single Sampling Plan | deep |
| Plans for inspection by variables for one-sided and two-sided specifications | nothing on this site teaches it | not here |
6 syllabus lines: 6 taught in depth, 0 at exam level, 0 not here yet.
| Syllabus line, as prescribed | Where it is taught here | Depth |
|---|---|---|
| Multivariate normal distribution and its properties; random sampling from it; maximum likelihood estimators of the parameters | Multivariate Analysis Unit 1 — Multinomial and Multivariate Normal Distributions | deep |
| Distribution of the sample mean vector; Wishart matrix and its distribution and properties | Multivariate Analysis Unit 2 — Wishart Distribution, Generalized Variance and Correlation Distributions | deep |
| Distribution of the sample generalized variance; null and non-null distribution of simple correlation coefficients | Multivariate Analysis Unit 2 — Wishart Distribution, Generalized Variance and Correlation Distributions | deep |
| Null distribution of partial and multiple correlation coefficients; distribution of the sample regression coefficients | Multivariate Analysis Unit 2 — Wishart Distribution, Generalized Variance and Correlation Distributions | deep |
| Hotelling's T-squared and its applications; Mahalanobis D-squared; classification and discrimination procedures | Multivariate Analysis Unit 3 — Hotelling's T-squared, Mahalanobis D-squared, Wilks' Lambda and Discriminant Analysis | deep |
| Principal component analysis; canonical variates and canonical correlation — definition, use, estimation and computation | Multivariate Analysis Unit 4 — Principal Components, Canonical Correlation, Clustering, Scaling and Factor Analysis | deep |
6 syllabus lines: 6 taught in depth, 0 at exam level, 0 not here yet.
6 syllabus lines: 6 taught in depth, 0 at exam level, 0 not here yet.
| Syllabus line, as prescribed | Where it is taught here | Depth |
|---|---|---|
| Basics of C: components, structure of a program, data types, enumerated and derived types | Data Science Problem Solving Using C | deep |
| Operators, control structures, arrays, functions, pointers, structures and file handling in C | Data Science Problem Solving Using C | deep |
| Basics of R: the environment, objects, vectors, matrices, lists and data frames; import and export | R Programming Unit 1 — Basics of R for Statistical Data Handling | deep |
| Descriptive statistics and graphics in R | R Programming Unit 2 — Descriptive Statistics in R | deep |
| Statistical tests, correlation and regression in R | R Programming Unit 4 — Inferential Statistics & Hypothesis Testing | deep |
| Building statistical programs in R without packages, and writing a statistical report | Data Handling using R — Practical | deep |
Not covered yet — 10 lines in Paper IV. Read these from a standard text; this site does not yet teach them.