In our every day lives we are faced with risk; the possibility of losing something of value. This could include theft or re to property, sickness, disability or even death. As loss adverse as we are, we tend to set up mediums to prevent or recover from losses once incurred. One of these common mediums is insurance. Anderson and Brown (2005) de nes insurance as an agreement where, for a stipulated payment called the premium, one party (the insurer) agrees to pay to the other (the policyholder or his designated bene ciary) a de ned amount (the claim payment or bene t) upon the occurrence of a speci c loss. These losses are realised as a result of the occurance of events that are random and not easily predictable. Since it is the business of
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It is also expedient to verify that the selected distribution e ectively models the data because anything short of almost accurate could prove detrimental to future predictions. Hogg and Klugman (1984) serves as a standard reference for this subject.
Adeleke and Ibiwoye (2011) used these same concepts to model claim sizes in personal line non- life insurance in Nigeria. They performed analysis of claim size to determine fair premium to ensure that the premium charged to individual members of the pool is equitable. The main lines of insurance discussed were re, motor, property, theft and armed robbery insurance. In the study, they determined appropriate statistical distribution to t claim amounts for the various lines of insurance listed above. The statistical distributions considered for their study were the exponential distribution, the pareto distribution, the gamma distribution, the weibull distribution and the lognormal distribution. These distributions are discussed below with why Adeleke and Ibiwoye
1
(2011) deemed them suitable for modeling insurance claim amount.
Exponential …show more content…
3
Adeleke and Ibiwoye (2011) began their analysis by obtaining the descriptive statistics for the claims data for each line of insurance. The descriptive statistics gave more information about which sta- tistical distribution would be more suitable for the data. To give more support to the exploratory methods of tting the data, they proceeded to plot a histogram of the data over a plot of the tted distributioins. The tted distributions were reduced to the Exponential, Lognormal, Weibull and
Gamma distributions. A more classical technique, the chi-squared goodness of t test to examine the goodness of t of these distributions. This test was chosen over because the Kolmogorov-Smirno test and its modi cation, the Anderson-Darling test, because they are non parametric.
Their results established that a Gamma distribution would be best for the Property, Fire and the
Commercial lines of insurance, lognormal for the Theft and Motor lines, while Weibull would best t the Armed Robbery line of insurance.
In conclusion, this study has exposed how statistical distributions can be used to t real data.
Stakeholders can base on this information obtained from the estimates to forecast claims to
It is also expedient to verify that the selected distribution e ectively models the data because anything short of almost accurate could prove detrimental to future predictions. Hogg and Klugman (1984) serves as a standard reference for this subject.
Adeleke and Ibiwoye (2011) used these same concepts to model claim sizes in personal line non- life insurance in Nigeria. They performed analysis of claim size to determine fair premium to ensure that the premium charged to individual members of the pool is equitable. The main lines of insurance discussed were re, motor, property, theft and armed robbery insurance. In the study, they determined appropriate statistical distribution to t claim amounts for the various lines of insurance listed above. The statistical distributions considered for their study were the exponential distribution, the pareto distribution, the gamma distribution, the weibull distribution and the lognormal distribution. These distributions are discussed below with why Adeleke and Ibiwoye
1
(2011) deemed them suitable for modeling insurance claim amount.
Exponential …show more content…
3
Adeleke and Ibiwoye (2011) began their analysis by obtaining the descriptive statistics for the claims data for each line of insurance. The descriptive statistics gave more information about which sta- tistical distribution would be more suitable for the data. To give more support to the exploratory methods of tting the data, they proceeded to plot a histogram of the data over a plot of the tted distributioins. The tted distributions were reduced to the Exponential, Lognormal, Weibull and
Gamma distributions. A more classical technique, the chi-squared goodness of t test to examine the goodness of t of these distributions. This test was chosen over because the Kolmogorov-Smirno test and its modi cation, the Anderson-Darling test, because they are non parametric.
Their results established that a Gamma distribution would be best for the Property, Fire and the
Commercial lines of insurance, lognormal for the Theft and Motor lines, while Weibull would best t the Armed Robbery line of insurance.
In conclusion, this study has exposed how statistical distributions can be used to t real data.
Stakeholders can base on this information obtained from the estimates to forecast claims to