# pareto: Moment function of Pareto Distribution (PDF:... In cascsim: Casualty Actuarial Society Individual Claim Simulator

## Description

Moment function of Pareto Distribution (PDF: alpha*xm^alpha/x^(alpha+1))

Density function of Pareto Distribution (PDF: alpha*xm^alpha/x^(alpha+1))

Cumulative probability function of Pareto Distribution (CDF: 1-(xm/x)^alpha)

Quantile function of Pareto Distribution

Random generation of Pareto Distribution

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```mpareto(order, xm, alpha = 3) dpareto(x, xm, alpha = 3) ppareto(q, xm, alpha = 3) qpareto(p, xm, alpha = 3) rpareto(n, xm, alpha = 3) ```

## Arguments

 `order` Order of moment `xm` Threshold value `alpha` Default=3 `x` Value of the variable `q` Value of the variable `p` Value of the probability `n` Number of samples

## Examples

 ```1 2 3 4 5``` ```mpareto(1,1000,2) dpareto(1500,1000,2) ppareto(1500,1000,2) qpareto(0.5,1000,2) rpareto(100,1000,2) ```

### Example output

```Attaching package: ‘cascsim’

The following object is masked from ‘package:base’:

truncate

[1] 2000
[1] 0.0005925926
[1] 0.5555556
[1] 1414.214
[1]  1283.420  1379.951  1921.252  1157.548  1178.861  1700.997  1368.888
[8]  5365.696  1163.687  1093.272  1077.954  1244.718  1152.913  4796.393
[15]  3422.013  1073.936  1027.291  1325.038  1454.968  1610.417  1011.889
[22]  4478.895 21923.678  1027.107  1382.126  1622.381  2205.005  1086.065
[29]  1891.892  1159.054  2124.373  1266.395  1143.506  3646.787  1181.449
[36]  1027.123  2129.249  1696.477  3300.654  2887.683  2090.503  1216.587
[43]  1238.965  1025.020  1276.399  1158.158 11061.832  1964.962  1411.893
[50]  1162.767  3925.108  1004.126  1181.529  1374.151  5266.262  1595.485
[57]  1328.877  1024.720  1242.508  1044.745  1400.741  1290.558  1111.806
[64]  4181.929  4087.839  1859.319  2400.729  1356.471  1640.264  1095.617
[71]  1282.240  1286.258  1026.145 14875.712  2880.005  1039.401  1640.198
[78]  1003.446  5144.789  1010.525  1307.259  1553.541  1159.448  1649.900
[85]  6585.743  1447.331  5148.169  1044.418  2201.049  1854.906  1417.983
[92]  2280.589  1060.798  1184.261  1333.874  2423.378  1314.582  1331.031
[99]  1206.282  2990.095
```

cascsim documentation built on Jan. 13, 2020, 5:07 p.m.