Fig 1.
Histogram showing livestock mortality in different asset bins, household livestock assets without insurance, and assets with a perfect insurance contract.
Each observation is a random draw from an underlying risk distribution for a household with about 1 tropical livestock unit expressed in US dollars ($); in this simplified example we only consider mortality, not herd growth through birth. See text for a description of the equations.
Fig 2.
Elements of insurance benefit: The shadow value of money (λ), insurance benefit (Δ), and an empirical distribution (histogram) of the probability of the livestock assets remaining after accounting for mortality expressed in USD.
To combine these measures on one figure, the y-axis was scaled to values shown on the figure.
Fig 3.
Livestock mortality in response to z-scores of (a) NOAA NDVI, (b) log(NOAA NDVI), (c) rainfall, (d) log(rainfall), (e) MODIS NDVI, and (f) log(MODIS NDVI) using linear regression (lm), piecewise linear regression when z-scores are less than zero (lm0) and -0.5 (lm5), and segmented regression (sm). Each observation corresponds to either the long or the short season of a sub-location in Marsabit.
Fig 4.
Assessment of the quality of an insurance index using R2 and the Relative Insurance Benefit (RIB) measure for different regression models (a & b) and remote sensing predictor variables (c & d). Four regression models were used: linear (lm), piecewise linear with z-scores less than 0 (lm0), piecewise linear with z-scores less than -0.5 (lm5), and segmented regression (sm). Data sources used as predictors were: Log MODIS NDVI (LMD), log NOAA NDVI (LNO), log rainfall (LRN), MODIS NDVI (MD), NOAA NDVI (NO), and rainfall (RN).
Fig 5.
Relationship between R2 and the relative insurance benefit (RIB) for the 24 combination of four regression modelling approaches: Linear (lm), piecewise linear with z-scores less than 0 (lm0), piecewise linear with z-scores less than -0.5 (lm5), and segmented regression (sm), using z-scores derived from six data sources: Log MODIS NDVI (LMD), log NOAA NDVI (LNO), log rainfall (LRN), MODIS NDVI (MD), NOAA NDVI (NO), and rainfall (RN).
Fig 6.
Quality of a hypothetical index insurance contract based on the segmented (sm) regression model with LMD data (R2 of 0.47 and RIB of 0.5) for 8 years and 15 sub-locations in Marsabit, Kenya (points), compared to a perfect insurance contract and to no insurance (lines).
The following classification was used for the contract: True Negatives: No payment due and none paid; Severe False Negatives: contract underpays by more than 30%; Intermediate False Negatives: contract underpays between 10% and 30%; Small False Negative: contract underpays less than 10%, and False Positives: contract overpays.
Fig 7.
Comparison of perfect insurance contract versus two index insurance contracts with similar R2 of 0.41 and RIB of 0.41 in (a) and 0.50 in (b). The index insurance contract in (a) in based on segmented (sm) model and lRN predictor while (b) uses piecewise linear with z-scores less than -0.5 (lm5) model and lMD predictor.
Fig 8.
Predictive skill of models used in Fig 7(A) and 7(B) respectively.
The red horizontal and vertical lines illustrates the mortality trigger at 23%.