Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [actuarial-science]

Questions relating to financial risk; often, but not limited to, insurance. This includes questions regarding stochastic distribution of cash flows, probability of ruin, financial payments above a threshold, etc.

Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in insurance, finance, and other industries and professions (Wikipedia 2021).

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Basic calculations with Order Statistics

I've come across the following problem, and I am tempted to delve into order statistics to solve this. I would greatly appreciate any help! Suppose you draw 6 independent samples from a continuous distribution. What is the approximate probability…
TheCuriouslyCodingFoxah
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Covid-19 and life expectancy

A public figure in my home country said the following: "The life expectancy in our country is 82 years. The average age of those who die of covid-19 is also about 82 years. Hence, on average, people do not die from covid-19 disease at all. I am…
Latent
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Calculate $\mathbb{P}[Y=y|X=x]$ where $X$ is the number of claims reported during first year and $Y$ is ultimate number of claims

A property-casualty insurance company issues automobile policies on a calendar year basis only. Let $X$ be a random variable representing the number of accident claims reported during calendar year 2005 on policies issued during calendar year 2005.…
Diego Fonseca
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Do good Cross-Validation results imply good QQ-plot results?

In Edward Frees' book Predictive Modeling Applications in Actuarial Science, Volume 2 the first chapter goes over how to build a frequency GLM model (using a Poisson distribution) on sample auto-insurance data. To test the data, they used cross…
platypus17
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Lee Carter mortality model - OLS (SVD) estimators if errors are heteroscedastic

In the classical Lee-Carter model, central death rates are modelled as follows: $\log(m(x,t)) = a(x) + b(x)\kappa(t) +\varepsilon(x,t)$ for some $x=0,\ldots,\omega$ and $t=1,\ldots, T$ and where $a(x)$, $b(x)$ and $k(t)$ are real-valued parameters…
Strickland
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Modeling bimodal time-to-event

Here is a plot of death registration frequencies by age for the UK in 1974. I see distributions like this quite often: there is some event (e.g. death) which happens either close to birth, or according to some other reasonably well-behaved…
R Hill
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What are good resources on nonlife actuarial science as it is being applied in industry?

I have already browsed my way through the book Nonlife Actuarial Models: Theory, Methods and Evaluation by Yiu-Kuen Tse and I am already familiar with nearly all of the underlying statistics in that book. However I don't know how relevant this book…
Meadowlark Bradsher
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Density of cost-per-loss random variable

Given a random variable $X$ with support $(a,b)$ and a value $d\in (a,b)$ (the "deductible"), the cost-per-loss random variable associated to $X$ is given by $$Y=\begin{cases}0&\text{if }X\le d\\ X&\text{if }X>d\end{cases}$$ According to this PDF,…
Castor
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How to combine state-level COVID-19 vaccination rates with national demographic data at the individual level?

I’m investigating possible correlations between the COVID-19 vaccination rate in the United States and the results of a long-running survey of scientific personality traits like "Agreeableness" and "Conscientiousness." While the survey does not ask…
Chris Wilson
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Independence of censoring time $C$ and event time $T$ for randomised entry to a study

While reading through the textbook 'Modern Applied Statistics With S' by Venables and Ripley, I came across the following paragraph detailing the different types of censoring possible when dealing with survival data. Highlighted is a sentence of…
Will
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Hazard rate from Weibull vs. cumulative hazard plot does not match

) My problem is that I have HR for a factor named "Selvrisiko" and I get the output estimates (HR) (Upper bound) (Lower bound) as: but when I plot (Kaplan - Meier) cumulative hazard for the groups I get: Interpretation: group 5262 and 7015 has…
Jesper Kristensen
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Copula partial derivates

I have some troubles with the demonstration of this theorem: Let C be a copula, for any v in I=[0,1] the partial derivative for u exists for almost (Lebesgue meaning) all u, and it is included between 0 and 1. Similarly for v. Furthermore these…
Laura
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Remediation for distributions with infinite moments

A colleague of mine posed a question to me regarding certain distributions used in loss models. Naturally occurring distributions, such as inverse Pareto, do not have finite moments. But naturally occurring questions within actuarial science, such…
Ryan Causey
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R - matrix optimization problem (Lee-Carter with MLE parameters)

I am trying to reproduce one of models evolved on the base of Lee-Carter model by use of RStudio. Because I am still pretty fresh in this software, my question is not really sophisticated. Applying MLE with Poisson distribution, I got final…
JJ-23
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Attempting to find mean of Weibull function in R

I am using a Weibull distribution in R, and know that: E(X) = 1000 and Var(X) = 500,000 Knowing: E(X^r) = ($\Gamma$(1+ (r/$\gamma$))) * 1/c^(r/$\gamma$)) I found the following parameters using the uniroot functions in R and obtained: c =…
Andre Croucher
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