Abstract
Consistent crop information is vital for the survival of the crop insurance sector, which relies on historical crop data, weather records, meteorological information, and farmers’ details. In India, fragmented, low-quality, and costly data have led to adverse claims ratios, forcing insurance companies to exit the market. This paper proposes an integrated framework that assimilates crop details, quality satellite data, and an actuarial model for crop yield estimation. We use kernel density estimation for risk assessment and emphasize the critical role of bandwidth calculation. Our research indicates that traditional heuristics for bandwidth selection can be misleading. A visualization of the fitted distribution with a frequency histogram can often provide tell-tale signs of an erroneous conclusion from the heuristics. We emphasize the role of the modeller’s judgment in determining the optimal bandwidth that is free from overfitting or over-smoothing. The framework bridges the gap between data and the insurer. The proposed model is of regulatory importance as it solves the issue of missing data and improves risk assessment, which will improve crop insurance market penetration and farmers’ participation and thereby promote stability in the crop insurance sector.
Acknowledgments
The authors thank the Indian Space Research Organisation (YS/PD-IP/343) and the University Grants Commission for financial support. We accessed all the remote sensing inputs, such as LAI, via GEE product MOD15A2H V6.1. Bhuvan provides Land Use maps at 1:50000 scale through a Web Map Tile Service.
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Research ethics: Not applicable.
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Informed consent: Not applicable.
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Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Use of Large Language Models, AI and Machine Learning Tools: The manuscript was reviewed for grammar and spelling using Grammarly.
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Conflict of interest: The authors state no conflict of interest.
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Research funding: The authors thank the Indian Space Research Organisation (YS/PD-IP/343) and the University Grants Commission for financial support.
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Data availability: Not applicable.
Annexure
AMISE comparison of four bandwidth selection methods for explanatory variables.
District | Variable | Method | ISE | AMISE |
---|---|---|---|---|
AMBALA | lai | Silverman | 0.00217 | 0.00011 |
AMBALA | lai | CV | 0.00000 | 0.00000 |
AMBALA | lai | Plug-in | 0.00249 | 0.00012 |
AMBALA | lai | Bootstrap | 0.00222 | 0.00011 |
AMBALA | phvstlai | Silverman | 0.01575 | 0.00087 |
AMBALA | phvstlai | CV | 0.00000 | 0.00000 |
AMBALA | phvstlai | Plug-in | 0.01777 | 0.00099 |
AMBALA | phvstlai | Bootstrap | 0.01615 | 0.00090 |
AMBALA | T2 | Silverman | 0.00349 | 0.00017 |
AMBALA | T2 | CV | 63.66198 | 3.18310 |
AMBALA | T2 | Plug-in | 0.00396 | 0.00020 |
AMBALA | T2 | Bootstrap | 0.00360 | 0.00018 |
BAGHPAT | lai | Silverman | 0.00091 | 0.00005 |
BAGHPAT | lai | CV | 0.00000 | 0.00000 |
BAGHPAT | lai | Plug-in | 0.00113 | 0.00006 |
BAGHPAT | lai | Bootstrap | 0.00094 | 0.00005 |
BAGHPAT | phvstlai | Silverman | 0.00734 | 0.00049 |
BAGHPAT | phvstlai | CV | 0.00000 | 0.00000 |
BAGHPAT | phvstlai | Plug-in | 0.01131 | 0.00075 |
BAGHPAT | phvstlai | Bootstrap | 0.00792 | 0.00053 |
BAGHPAT | T2 | Silverman | 0.00299 | 0.00017 |
BAGHPAT | T2 | CV | 48.51545 | 2.69530 |
BAGHPAT | T2 | Plug-in | 0.00381 | 0.00021 |
BAGHPAT | T2 | Bootstrap | 0.00313 | 0.00017 |
BHIWANI | lai | Silverman | 0.00036 | 0.00002 |
BHIWANI | lai | CV | 0.00000 | 0.00000 |
BHIWANI | lai | Plug-in | 0.00041 | 0.00002 |
BHIWANI | lai | Bootstrap | 0.00037 | 0.00002 |
BHIWANI | phvstlai | Silverman | 0.05017 | 0.00279 |
BHIWANI | phvstlai | CV | 148.85111 | 8.26951 |
BHIWANI | phvstlai | Plug-in | 0.05564 | 0.00309 |
BHIWANI | phvstlai | Bootstrap | 0.05182 | 0.00288 |
BHIWANI | T2 | Silverman | 0.00225 | 0.00011 |
BHIWANI | T2 | CV | 63.66198 | 3.18310 |
BHIWANI | T2 | Plug-in | 0.00269 | 0.00013 |
BHIWANI | T2 | Bootstrap | 0.00233 | 0.00012 |
BIJNOR | lai | Silverman | 0.02483 | 0.00131 |
BIJNOR | lai | CV | 21.88210 | 1.15169 |
BIJNOR | lai | Plug-in | 0.02917 | 0.00154 |
BIJNOR | lai | Bootstrap | 0.02558 | 0.00135 |
BIJNOR | phvstlai | Silverman | 0.00462 | 0.00027 |
BIJNOR | phvstlai | CV | 0.00000 | 0.00000 |
BIJNOR | phvstlai | Plug-in | 0.00526 | 0.00031 |
BIJNOR | phvstlai | Bootstrap | 0.00476 | 0.00028 |
BIJNOR | T2 | Silverman | 0.00468 | 0.00025 |
BIJNOR | T2 | CV | 107.47028 | 5.65633 |
BIJNOR | T2 | Plug-in | 0.00664 | 0.00035 |
BIJNOR | T2 | Bootstrap | 0.00486 | 0.00026 |
FARIDABAD | lai | Silverman | 0.00090 | 0.00004 |
FARIDABAD | lai | CV | 0.00000 | 0.00000 |
FARIDABAD | lai | Plug-in | 0.00106 | 0.00005 |
FARIDABAD | lai | Bootstrap | 0.00093 | 0.00005 |
FARIDABAD | phvstlai | Silverman | 0.13049 | 0.00725 |
FARIDABAD | phvstlai | CV | 58.48907 | 3.24939 |
FARIDABAD | phvstlai | Plug-in | 0.29252 | 0.01625 |
FARIDABAD | phvstlai | Bootstrap | 0.13841 | 0.00769 |
FARIDABAD | T2 | Silverman | 0.00245 | 0.00012 |
FARIDABAD | T2 | CV | 63.66198 | 3.18310 |
FARIDABAD | T2 | Plug-in | 0.00273 | 0.00014 |
FARIDABAD | T2 | Bootstrap | 0.00251 | 0.00013 |
FATEHBAD | lai | Silverman | 0.00021 | 0.00001 |
FATEHBAD | lai | CV | 0.00000 | 0.00000 |
FATEHBAD | lai | Plug-in | 0.00027 | 0.00001 |
FATEHBAD | lai | Bootstrap | 0.00022 | 0.00001 |
FATEHBAD | phvstlai | Silverman | 0.10059 | 0.00559 |
FATEHBAD | phvstlai | CV | 29.25794 | 1.62544 |
FATEHBAD | phvstlai | Plug-in | 0.15226 | 0.00846 |
FATEHBAD | phvstlai | Bootstrap | 0.10550 | 0.00586 |
FATEHBAD | T2 | Silverman | 0.00268 | 0.00013 |
FATEHBAD | T2 | CV | 83.55635 | 4.17782 |
FATEHBAD | T2 | Plug-in | 0.00328 | 0.00016 |
FATEHBAD | T2 | Bootstrap | 0.00279 | 0.00014 |
GHAZIABAD | lai | Silverman | 0.00236 | 0.00012 |
GHAZIABAD | lai | CV | 0.00000 | 0.00000 |
GHAZIABAD | lai | Plug-in | 0.00269 | 0.00014 |
GHAZIABAD | lai | Bootstrap | 0.00242 | 0.00013 |
GHAZIABAD | phvstlai | Silverman | 0.00981 | 0.00058 |
GHAZIABAD | phvstlai | CV | 49.68456 | 2.92262 |
GHAZIABAD | phvstlai | Plug-in | 0.01075 | 0.00063 |
GHAZIABAD | phvstlai | Bootstrap | 0.01000 | 0.00059 |
GHAZIABAD | T2 | Silverman | 0.00199 | 0.00010 |
GHAZIABAD | T2 | CV | 73.27519 | 3.85659 |
GHAZIABAD | T2 | Plug-in | 0.00215 | 0.00011 |
GHAZIABAD | T2 | Bootstrap | 0.00204 | 0.00011 |
HISAR | lai | Silverman | 0.00063 | 0.00003 |
HISAR | lai | CV | 35.45927 | 1.77296 |
HISAR | lai | Plug-in | 0.00079 | 0.00004 |
HISAR | lai | Bootstrap | 0.00066 | 0.00003 |
HISAR | phvstlai | Silverman | 0.05386 | 0.00299 |
HISAR | phvstlai | CV | 0.57158 | 0.03175 |
HISAR | phvstlai | Plug-in | 0.09238 | 0.00513 |
HISAR | phvstlai | Bootstrap | 0.05909 | 0.00328 |
HISAR | T2 | Silverman | 0.00366 | 0.00018 |
HISAR | T2 | CV | 63.66198 | 3.18310 |
HISAR | T2 | Plug-in | 0.00620 | 0.00031 |
HISAR | T2 | Bootstrap | 0.00383 | 0.00019 |
KAITHAL | lai | Silverman | 0.00052 | 0.00003 |
KAITHAL | lai | CV | 0.00000 | 0.00000 |
KAITHAL | lai | Plug-in | 0.00065 | 0.00003 |
KAITHAL | lai | Bootstrap | 0.00054 | 0.00003 |
KAITHAL | phvstlai | Silverman | 0.02373 | 0.00132 |
KAITHAL | phvstlai | CV | 0.00037 | 0.00002 |
KAITHAL | phvstlai | Plug-in | 0.23771 | 0.01321 |
KAITHAL | phvstlai | Bootstrap | 0.02618 | 0.00145 |
KAITHAL | T2 | Silverman | 0.00227 | 0.00011 |
KAITHAL | T2 | CV | 561.02117 | 28.05106 |
KAITHAL | T2 | Plug-in | 0.00272 | 0.00014 |
KAITHAL | T2 | Bootstrap | 0.00233 | 0.00012 |
KARNAL | lai | Silverman | 0.00200 | 0.00010 |
KARNAL | lai | CV | 18.21586 | 0.91079 |
KARNAL | lai | Plug-in | 0.00283 | 0.00014 |
KARNAL | lai | Bootstrap | 0.00207 | 0.00010 |
KARNAL | phvstlai | Silverman | 0.03129 | 0.00174 |
KARNAL | phvstlai | CV | 0.00000 | 0.00000 |
KARNAL | phvstlai | Plug-in | 0.03558 | 0.00198 |
KARNAL | phvstlai | Bootstrap | 0.03243 | 0.00180 |
KARNAL | T2 | Silverman | 0.00199 | 0.00010 |
KARNAL | T2 | CV | 63.66198 | 3.18310 |
KARNAL | T2 | Plug-in | 0.00211 | 0.00011 |
KARNAL | T2 | Bootstrap | 0.00201 | 0.00010 |
KURUKSHETRA | lai | Silverman | 0.00220 | 0.00011 |
KURUKSHETRA | lai | CV | 0.00000 | 0.00000 |
KURUKSHETRA | lai | Plug-in | 0.00252 | 0.00013 |
KURUKSHETRA | lai | Bootstrap | 0.00227 | 0.00011 |
KURUKSHETRA | phvstlai | Silverman | 0.00990 | 0.00055 |
KURUKSHETRA | phvstlai | CV | 7.11974 | 0.39554 |
KURUKSHETRA | phvstlai | Plug-in | 0.01194 | 0.00066 |
KURUKSHETRA | phvstlai | Bootstrap | 0.01025 | 0.00057 |
KURUKSHETRA | T2 | Silverman | 0.00223 | 0.00011 |
KURUKSHETRA | T2 | CV | 63.66198 | 3.18310 |
KURUKSHETRA | T2 | Plug-in | 0.00247 | 0.00012 |
KURUKSHETRA | T2 | Bootstrap | 0.00228 | 0.00011 |
MORADABAD | lai | Silverman | 0.00169 | 0.00009 |
MORADABAD | lai | CV | 0.00000 | 0.00000 |
MORADABAD | lai | Plug-in | 0.00191 | 0.00010 |
MORADABAD | lai | Bootstrap | 0.00173 | 0.00009 |
MORADABAD | phvstlai | Silverman | 0.00541 | 0.00032 |
MORADABAD | phvstlai | CV | 0.00000 | 0.00000 |
MORADABAD | phvstlai | Plug-in | 0.00750 | 0.00044 |
MORADABAD | phvstlai | Bootstrap | 0.00558 | 0.00033 |
MORADABAD | T2 | Silverman | 0.00269 | 0.00014 |
MORADABAD | T2 | CV | 246.69315 | 12.98385 |
MORADABAD | T2 | Plug-in | 0.00311 | 0.00016 |
MORADABAD | T2 | Bootstrap | 0.00277 | 0.00015 |
MUZZAFARNAGAR | lai | Silverman | 0.00818 | 0.00043 |
MUZZAFARNAGAR | lai | CV | 0.00000 | 0.00000 |
MUZZAFARNAGAR | lai | Plug-in | 0.00921 | 0.00048 |
MUZZAFARNAGAR | lai | Bootstrap | 0.00837 | 0.00044 |
MUZZAFARNAGAR | phvstlai | Silverman | 0.00786 | 0.00046 |
MUZZAFARNAGAR | phvstlai | CV | 0.23208 | 0.01365 |
MUZZAFARNAGAR | phvstlai | Plug-in | 0.01155 | 0.00068 |
MUZZAFARNAGAR | phvstlai | Bootstrap | 0.00821 | 0.00048 |
MUZZAFARNAGAR | T2 | Silverman | 0.00295 | 0.00016 |
MUZZAFARNAGAR | T2 | CV | 95.25775 | 5.01357 |
MUZZAFARNAGAR | T2 | Plug-in | 0.00359 | 0.00019 |
MUZZAFARNAGAR | T2 | Bootstrap | 0.00309 | 0.00016 |
PILIBHIT | lai | Silverman | 0.00107 | 0.00006 |
PILIBHIT | lai | CV | 0.00000 | 0.00000 |
PILIBHIT | lai | Plug-in | 0.00122 | 0.00006 |
PILIBHIT | lai | Bootstrap | 0.00109 | 0.00006 |
PILIBHIT | phvstlai | Silverman | 0.00236 | 0.00014 |
PILIBHIT | phvstlai | CV | 0.00000 | 0.00000 |
PILIBHIT | phvstlai | Plug-in | 0.00276 | 0.00016 |
PILIBHIT | phvstlai | Bootstrap | 0.00247 | 0.00015 |
PILIBHIT | T2 | Silverman | 0.00415 | 0.00022 |
PILIBHIT | T2 | CV | 95.25775 | 5.01357 |
PILIBHIT | T2 | Plug-in | 0.00584 | 0.00031 |
PILIBHIT | T2 | Bootstrap | 0.00427 | 0.00022 |
RAMPUR | lai | Silverman | 0.00034 | 0.00002 |
RAMPUR | lai | CV | 0.00000 | 0.00000 |
RAMPUR | lai | Plug-in | 0.00047 | 0.00002 |
RAMPUR | lai | Bootstrap | 0.00036 | 0.00002 |
RAMPUR | phvstlai | Silverman | 0.00270 | 0.00016 |
RAMPUR | phvstlai | CV | 0.00000 | 0.00000 |
RAMPUR | phvstlai | Plug-in | 0.00327 | 0.00019 |
RAMPUR | phvstlai | Bootstrap | 0.00279 | 0.00016 |
RAMPUR | T2 | Silverman | 0.00252 | 0.00013 |
RAMPUR | T2 | CV | 95.25775 | 5.01357 |
RAMPUR | T2 | Plug-in | 0.00285 | 0.00015 |
RAMPUR | T2 | Bootstrap | 0.00258 | 0.00014 |
SONIPAT | lai | Silverman | 0.00029 | 0.00001 |
SONIPAT | lai | CV | 0.00000 | 0.00000 |
SONIPAT | lai | Plug-in | 0.00038 | 0.00002 |
SONIPAT | lai | Bootstrap | 0.00031 | 0.00002 |
SONIPAT | phvstlai | Silverman | 0.05701 | 0.00317 |
SONIPAT | phvstlai | CV | 0.00000 | 0.00000 |
SONIPAT | phvstlai | Plug-in | 0.13789 | 0.00766 |
SONIPAT | phvstlai | Bootstrap | 0.06002 | 0.00333 |
SONIPAT | T2 | Silverman | 0.00238 | 0.00012 |
SONIPAT | T2 | CV | 218.83805 | 10.94190 |
SONIPAT | T2 | Plug-in | 0.00264 | 0.00013 |
SONIPAT | T2 | Bootstrap | 0.00243 | 0.00012 |
Bandwidth value under Silverman’s method.
District | Variable | Method | Bandwidth |
---|---|---|---|
Ambala | T2 | Silverman | 0.84 |
Ambala | lai | Silverman | 1.17 |
Ambala | phvstlai | Silverman | 0.41 |
Baghpat | T2 | Silverman | 0.87 |
Baghpat | lai | Silverman | 0.77 |
Baghpat | phvstlai | Silverman | 0.68 |
Bhiwani | T2 | Silverman | 0.78 |
Bhiwani | lai | Silverman | 2.07 |
Bhiwani | phvstlai | Silverman | 0.20 |
Bijnor | T2 | Silverman | 0.85 |
Bijnor | lai | Silverman | 0.33 |
Bijnor | phvstlai | Silverman | 0.61 |
Faridabad | T2 | Silverman | 0.79 |
Faridabad | lai | Silverman | 1.44 |
Faridabad | phvstlai | Silverman | 0.21 |
Fatehbad | T2 | Silverman | 0.88 |
Fatehbad | lai | Silverman | 2.64 |
Fatehbad | phvstlai | Silverman | 0.20 |
Ghaziabad | T2 | Silverman | 0.80 |
Ghaziabad | lai | Silverman | 0.79 |
Ghaziabad | phvstlai | Silverman | 0.56 |
Hisar | T2 | Silverman | 0.98 |
Hisar | lai | Silverman | 2.13 |
Hisar | phvstlai | Silverman | 0.27 |
Kaithal | T2 | Silverman | 0.82 |
Kaithal | lai | Silverman | 2.05 |
Kaithal | phvstlai | Silverman | 0.63 |
Karnal | T2 | Silverman | 0.80 |
Karnal | lai | Silverman | 1.26 |
Karnal | phvstlai | Silverman | 0.27 |
Kurukshetra | T2 | Silverman | 0.86 |
Kurukshetra | lai | Silverman | 1.00 |
Kurukshetra | phvstlai | Silverman | 0.54 |
Moradabad | T2 | Silverman | 0.84 |
Moradabad | lai | Silverman | 0.94 |
Moradabad | phvstlai | Silverman | 0.60 |
Muzzafarnagar | T2 | Silverman | 0.89 |
Muzzafarnagar | lai | Silverman | 0.43 |
Muzzafarnagar | phvstlai | Silverman | 0.55 |
Pilibhit | T2 | Silverman | 0.86 |
Pilibhit | lai | Silverman | 1.12 |
Pilibhit | phvstlai | Silverman | 0.99 |
Rampur | T2 | Silverman | 0.83 |
Rampur | lai | Silverman | 1.53 |
Rampur | phvstlai | Silverman | 0.65 |
Sonipat | T2 | Silverman | 0.86 |
Sonipat | lai | Silverman | 2.10 |
Sonipat | phvstlai | Silverman | 0.30 |
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Articles in the same Issue
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Articles in the same Issue
- Frontmatter
- Featured Articles (Research Paper)
- Net Reserve Calculation for Whole Life Insurance Under Mean-Reverting Stochastic Interest Rate Models
- Integrating Remote Sensing Data in Crop Insurance: A Solution to Data Scarcity in India
- How do Consumers Think About Usage-Based Auto Insurance? –A Survey Analysis from Taiwan
- Measurement of Risk Culture in General Insurance Companies in India – An Empirical Validation Using a Causal Model