ICAR-IASRI MSc and PhD (Agricultural Statistics, Computer Application, Bioinformatics) · India · ICAR-Indian Agricultural Statistics Research Institute with the IARI Graduate School
Original practice questions written to the published syllabus · not past papersThe numbers behind crop and livestock insurance: loss distributions, premium principles, credibility theory and ruin probability, then their agricultural use in area-yield index design, threshold yield and indemnity levels, premium rating from yield and weather histories, basis risk in weather-index insurance, and the sampling of crop-cutting experiments for claims. Scheme-level insurance management is in the Agribusiness track.
In the exams: ICAR MSc elective (actuarial statistics); light in national exams; crop-insurance analytics roles (applied)
ICAR-IASRI MSc and PhD programmes (actuarial statistics elective)
Loss distributions, premium principles, credibility (limited fluctuation and Buhlmann), ruin probability, and the design and rating of area-yield and weather-index crop insurance.
How our questions for ICAR-IASRI MSc and PhD spread across the units of Actuarial Statistics & Crop Insurance Design. Difficulty: 25 easy, 48 medium, 18 hard.
| Loss distributions and fitting to claims data | 10 | |
| Weather-index insurance: index construction and basis risk | 10 | |
| Number of crop-cutting experiments needed for claim settlement | 10 | |
| Premium principles and risk loading | 9 | |
| Ruin theory and reserves (introduction) | 9 | |
| Area-yield index insurance: unit area and threshold yield | 9 | |
| Livestock mortality insurance and life-table methods | 9 | |
| Use of remote sensing and technology in claim assessment | 9 | |
| Credibility theory | 8 | |
| Yield detrending and premium rating from historical yields | 8 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
Claims above a policy limit are recorded only as the limit. In maximum likelihood fitting, how do these capped observations contribute?
B. Via the probability of exceeding it
Capped claims are right-censored; each contributes 1 - F(u). Treating them as exact losses equal to u, or dropping them, biases the tail.
Further reading: Klugman, Panjer and Willmot, Loss Models
A block's crop insurance paid 60,000,000 currency units in claims on a total sum insured of 500,000,000. What is the loss cost ratio?
B. 12 per cent
Loss cost ratio = indemnity / liability = 6/50 = 12%. 8.3 inverts the ratio; 0.12 per cent mixes the proportion with a percentage.
Further reading: Klugman, Panjer and Willmot, Loss Models
What is the statistical trade-off in reducing the size of the insurance unit?
C. Less basis risk, more sampling cost
Smaller units track farm yields better, but each unit's yield needs its own crop-cutting experiments, raising cost and the sampling error per unit for a given total effort.
Further reading: Halcrow (1949); Skees, Black and Barnett (1997)
A rainfall-deficit contract has a trigger of 300 mm, an exit of 100 mm and a sum insured of 20,000 currency units, paid linearly between them. What is the payout rate per mm?
C. 100 currency units
Tick = sum insured / (trigger - exit) = 20,000/200 = 100. Dividing by the trigger gives 66.7.
Further reading: World Bank (2011), Weather Index Insurance for Agriculture
Why are index contracts often split into crop phases, each with its own trigger?
D. A shortfall matters more at certain stages
Rainfall deficits at sowing or flowering hurt yield more than at other times; phase-wise indices match the crop's sensitivity.
Further reading: World Bank (2011), Weather Index Insurance for Agriculture
An animal has a 4 per cent chance of death in the policy year and a sum insured of 50,000 currency units. What is the pure premium?
A. 2,000 currency units
Pure premium = 0.04 x 50,000 = 2,000.
Further reading: Klugman et al., Loss Models; standard life-table methods
Why is a flat premium rate for all ages of cattle problematic?
D. Mortality varies with age
Mortality is high in young calves and rises in old animals, so a flat rate over-charges some ages and under-charges others; it cross-subsidises and invites adverse selection.
Further reading: Klugman et al., Loss Models; standard life-table methods
With a coefficient of variation of plot yields of 40 per cent, how many crop-cutting experiments give a 95 per cent margin of 20 per cent of the mean?
C. 16
(1.96 x 40/20)^2 = 15.4, so 16. 62 is the requirement for a 10% margin.
Further reading: Cochran, Sampling Techniques
A technology yield model systematically underestimates losses in rainfed smallholder areas with frequent cloud cover. Why is this especially serious?
A. It hurts the most vulnerable farmers
Systematic bias by farm type is an equity problem, not just an accuracy one; models must be tested for bias across groups.
Further reading: World Bank (2011); remote-sensing crop monitoring literature
Which technology suits assessment of localised damage such as hail on a few fields?
A. High-resolution drone imagery
Drones resolve field-scale damage that coarse satellite pixels average away.
Further reading: World Bank (2011); remote-sensing crop monitoring literature
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