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comprised of 2500 insureds: | comprised of 2500 insureds: | ||
#<math>X_i = \sum_{j=1}^{N_i}Y_{ij} </math> is a random variable representing the annual loss of the i< | #<math>X_i = \sum_{j=1}^{N_i}Y_{ij} </math> is a random variable representing the annual loss of the i<sup>th</sup> insured. | ||
#<math>N_1,N_2,\ldots,N_{2500}</math> are independent and identically distributed random variables following a negative binomial distribution with parameters <math>r = 2</math> and <math>\beta = 0.2</math>. | #<math>N_1,N_2,\ldots,N_{2500}</math> are independent and identically distributed random variables following a negative binomial distribution with parameters <math>r = 2</math> and <math>\beta = 0.2</math>. | ||
#<math>Y_{i1},Y_{i2},\ldots,Y_{iN}</math> are independent and identically distributed random variables following a Pareto distribution with <math>\alpha = 3</math> and <math>\theta = 1000 </math>. | #<math>Y_{i1},Y_{i2},\ldots,Y_{iN}</math> are independent and identically distributed random variables following a Pareto distribution with <math>\alpha = 3</math> and <math>\theta = 1000 </math>. | ||
Latest revision as of 16:09, 13 May 2023
You are given the following information about a general liability book of business comprised of 2500 insureds:
- [math]X_i = \sum_{j=1}^{N_i}Y_{ij} [/math] is a random variable representing the annual loss of the ith insured.
- [math]N_1,N_2,\ldots,N_{2500}[/math] are independent and identically distributed random variables following a negative binomial distribution with parameters [math]r = 2[/math] and [math]\beta = 0.2[/math].
- [math]Y_{i1},Y_{i2},\ldots,Y_{iN}[/math] are independent and identically distributed random variables following a Pareto distribution with [math]\alpha = 3[/math] and [math]\theta = 1000 [/math].
- The full credibility standard is to be within 5% of the expected aggregate losses 90% of the time.
Calculate the partial credibility of the annual loss experience for this book of business using limited fluctuation credibility theory.
- 0.34
- 0.42
- 0.47
- 0.50
- 0.53
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.