MackChainladder Example

import pandas as pd
import chainladder as cl

This example demonstrates how you can use the Mack Chainladder method.

# Load the data
data = cl.load_sample("raa")

# Compute Mack Chainladder ultimates and Std Err using 'mack' interpolation
# This recreates the figures from page 130 of Mack (1994)
mack = cl.MackChainladder()
dev = cl.Development(sigma_interpolation="mack")
mack.fit(dev.fit_transform(data))

plot_data = mack.summary_.to_frame(origin_as_datetime=False)
plot_data

	Latest	IBNR	Ultimate	Mack Std Err
1981	18834.0	NaN	18834.000000	NaN
1982	16704.0	153.953917	16857.953917	206.220059
1983	23466.0	617.370924	24083.370924	623.376673
1984	27067.0	1636.142163	28703.142163	747.175225
1985	26180.0	2746.736343	28926.736343	1469.457150
1986	15852.0	3649.103184	19501.103184	2001.856931
1987	12314.0	5435.302590	17749.302590	2209.242094
1988	13112.0	10907.192510	24019.192510	5357.869298
1989	5395.0	10649.984101	16044.984101	6333.165866
1990	2063.0	16339.442529	18402.442529	24566.287911

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import matplotlib.pyplot as plt

plt.style.use("ggplot")
%config InlineBackend.figure_format = 'retina'

ax = plot_data[["Latest", "IBNR"]].plot(
    kind="bar",
    stacked=True,
    ylim=(0, None),
    grid=True,
    yerr=pd.DataFrame({
        "latest": plot_data["Mack Std Err"] * 0,
        "IBNR": plot_data["Mack Std Err"],
    }),
    title="Mack Chainladder Ultimate",
    xlabel="Accident Year",
    ylabel="Loss",
);