Description Usage Arguments Details Value Author(s) References Examples

`mln.am`

is the probability density function of a mixture of three lognormal densities.

1 | ```
dmln.am(x, u.1, u.2, u.3, sigma.1, sigma.2, sigma.3, p.1, p.2)
``` |

`x` |
value at which the denisty is to be evaluated |

`u.1` |
log mean of the first lognormal |

`u.2` |
log mean of the second lognormal |

`u.3` |
log mean of the third lognormal |

`sigma.1` |
log standard deviation of the first lognormal |

`sigma.2` |
log standard deviation of the second lognormal |

`sigma.3` |
log standard deviation of the third lognormal |

`p.1` |
weight assigned to the first density |

`p.2` |
weight assigned to the second density |

mln is density f(x) = p.1 * f1(x) + p.2 * f2(x) + (1 - p.1 - p.2) * f3(x), where f1, f2, and f3 are lognormal densities with log means u.1,u.2, and u.3 and standard deviations sigma.1, sigma.2, and sigma.3 respectively.

`out ` |
density value at x |

Kam Hamidieh

Melick, W. R. and Thomas, C. P. (1997). Recovering an asset's implied pdf from option prices: An
application to crude oil during the gulf crisis. *Journal of Financial and Quantitative Analysis*,
32(1), 91-115.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ```
###
### Just look at a generic density and see if it integrates to 1.
###
u.1 = 4.2
u.2 = 4.5
u.3 = 4.8
sigma.1 = 0.30
sigma.2 = 0.20
sigma.3 = 0.15
p.1 = 0.25
p.2 = 0.45
x = seq(from = 0, to = 250, by = 0.01)
y = dmln.am(x = x, u.1 = u.1, u.2 = u.2, u.3 = u.3, sigma.1 = sigma.1, sigma.2 = sigma.2,
sigma.3 = sigma.3, p.1 = p.1, p.2 = p.2)
plot(y ~ x, type="l")
sum(y * 0.01)
###
### Yes, the sum is near 1.
###
``` |

```
[1] 0.9999984
```

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