ResearchArticle On Compound Distributions for Natural Disaster Modelling in Kenya Antony Rono, Carolyne Ogutu , and Patrick Weke SchoolofMathematics,UniversityofNairobi,Nairobi,Kenya CorrespondenceshouldbeaddressedtoCarolyneOgutu;cogutu@uonbi.ac.ke Received 10 February 2020; Accepted 4 April 2020; Published 25 April 2020 AcademicEditor:HernandoQuevedo Copyright©2020AntonyRonoetal.isisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Kenyancommunitiesareexposedtonaturaldisastersbyanamalgamationoffactorssuchaspoverty,aridity,andsettlementsin areassusceptibletonaturaldisastersorinareaswithpoorinfrastructure.isisexpectedtoincreaseduetotheeffectsofclimate change.Inanattempttoexplainsomeofthesevariabilities,wemodeltheextremedamagesfromnaturaldisastersinKenyaby developing a compound distribution that takes into account both the frequency and the severity of the extreme events. e resultingdistributionisbasedonathresholdmodelandcompoundextremevaluedistribution.Forfrequencyofeventsexceeding athresholdof150,000,wefoundthatitfollowsanegativebinomialdistribution,whileseverityofexceedancefollowsageneralized Paretodistribution.isdistributionfitsthedatawellandisfoundtobeabettermodelfornaturaldisastersinKenyathanthe traditional extreme value threshold model. 1. Introduction Kenya has continued to face an increasing vulnerability to natural disaster risk. e communities are exposed to nat- uraldisastersbyanamalgamationoffactorssuchaspoverty, aridity, and settlements in areas susceptible to natural di- sasters or in areas with poor infrastructure. ese factors coupled with naturally occurring hazards, which are cur- rently being propelled by climate change, pose an extreme threattotheKenyansociety.Asof2018,atotalof113natural disaster events had been recorded in the last six decades, affecting approximately 62 million people and resulting to 6,900 deaths. e total damage from these occurrences is estimatedtobe609millionUSdollars.Mostofthenatural disaster events are weather-related, with almost 70% of the landmassbeingaffectedbydroughtandatotalof55flooding events recorded in various parts of the country. As with most parts of the world, natural disasters are expected to increase in the future due to climate change. WorldBankprojectsthenumberofdroughtdaysinmany partsoftheworldtoincreasebymorethan20%by2080,and thenumberofpeopleexposedtodroughtcouldincreaseby 9 − 17% in 2030 and 50 − 90% in 2080. e number of peopleexposedtoriverfloodscouldalsoincreaseby4 − 15% in2030and12 − 29%in2080[1].However,theeffectswould befeltmostlyintheless-developedcountrieslikeKenya.A study conducted by the Center of Research and Epidemi- ology of Disasters (CRED) found that people living in the poorernationsaresixtimesmorelikelytobeinjured,tolose their homes, be displaced, or require emergency assistance thanthoseinthewealthiernations.eyarealsoseventimes morelikelytodiefromanaturaldisasterthanthoseinricher nations. erefore, with the increasing frequency and po- tential damage of natural disasters in Kenya, there is an urgentneedtounderstandthecharacteristicsofsuchevents in the country. In modelling extremal and rare events, extreme value theorem(EVT)emergesasavitaltooltomodelsuchrisks. ere are two main approaches in EVT: classical EVT (block-maxima) and excess over threshold (EOT) [2]. Several studies have been conducted on EVT and its ap- plicationtomodelnaturaldisastersincludingEngelandetal. [3] who used the block maxima method to model hydro- logical floods and droughts in the USA and Jindrova and Pacakova [4] who used EOT to model historical natural catastrophe losses in the USA. In both studies, they found Hindawi International Journal of Mathematics and Mathematical Sciences Volume 2020, Article ID 9398309, 8 pages https://doi.org/10.1155/2020/9398309