An Actuary’s Outlook

choi

Jordan Ellenberg, Life Actuarily. The risks of ecstasy (the drug) and equasy (the practice of  horse riding) are roughly the same. But most people don’t treat them that way. Wall Street Journal, June 3, 2014
online.wsj.com/articles/book-review-the-norm-chronicles-by-michael-blastland-and-david-spiegelhalter-1401751847
(book review on Michael Blastland and David Spiegelhalter, The Norm Chronicle; Stories and numbers about danger and death. Basic Books, 2014)

Note:
(a)
(i) actuarily (adv): "in the manner of, or using the methods of an actuary"
en.wiktionary.org/wiki/actuarily
(ii) I can not find “equasy” in any English dictionary.
(Latin English dictionary
equus (noun masculine): Horse”)

(b) “MicroLives, each MicroLife being one-millionth of a typical life span, or about 30 minutes of existence.”

The “30 minutes” times a million is 30 million minutes (for a lifetime). A day has 60 minutes times 24 hours, or 1440 minutes; a year (365.25 days) has 525,960 minutes.  THEREFORE 30m minutes equate 57.04 years!

(c) “Smoking a pack a day robs you of 10 MicroLives daily”
(i) In author’s own word:  
(A) David Spiegelhalter, Using Speed of Ageing and 'Microlives' to Communicate the Effects of Lifetime Habits and Environment. BMJ (British Medical Journal) 345:e8223 (2012)
understandinguncertainty.org/files/2012bmj-microlives.pdf
("Smoking works out at about 10 microlives for every 20 cigarettes smoked, around 15 minutes per cigarette (a previous basic analysis estimated 11 minutes pro rata loss in life expectancy per cigarette)
(B) Errata (but I do not see a table in (i)).
BMJ 345:e8223 (2012)
www.bmj.com/content/345/bmj.e8676
(ii) In other words, the WSJ book review states “smoking a pack a day” shorten life span by five hours (a cigarette costs 15 minutes or 0.5 microlife; 20 cigarettes equates 300 minutes or five hours).

(c) “What about that four-murder day, for instance? Homicides in London come at a rate of about 170 a year, or one every other day. * * * Clusters of rare events like murders are governed, absent complicating factors, by the so-called Poisson distribution. If murders were strewn around the calendar at random, subject only to the constraint that there is an average of 170 a year, you'd find that, with surprising regularity, 64% of days had no murder at all, 28% had exactly one and the remaining 8% had two or more.
The great miracle of probability theory is that random events, which might seem mathematically ungovernable by their very nature, are in fact subject to predictable regularities like this. And indeed, the London homicide data conforms almost exactly to what Poisson predicts. As for four-murder days, they should come about once every three years; in other words, surprising when they happen, but not indicative of any welling up of violence.”
(i) French English dictionary
poisson (noun masculine): “fish”
(ii) The Poisson Distribution. University of Massachusetts Amherst
www.umass.edu/wsp/resources/poisson/

Quote:

“Where the rate of occurrence of some event, r [the example here: on average 4 letters delivered a day] (in this chart called lambda or l [this is English letter "L" in lower case (not upper case "I") which corresponds to Greek letter lambda]) is small, the range of likely possibilities will lie near the zero line. Meaning that when the rate r is small, zero is a very likely number to get. As the rate becomes higher (as the occurrence of the thing we are watching becomes commoner), the center of the curve moves toward the right, and eventually, somewhere around r = 7, zero occurrences actually become unlikely. This is how the Poisson world looks graphically. All of it is intuitively obvious.

“For small values of p, the Poisson Distribution can simulate the Binomial Distribution (the pattern of Heads and Tails in coin tosses), and it is much easier to compute. * * * it is possible to count how many events have occurred, such as the number of times a firefly lights up in my garden in a given 5 seconds, some evening, but meaningless to ask how many such events have not occurred. This last point sums up the contrast with the Binomial situation, where the probability of each of two mutually exclusive events (p and q) is known. The Poisson Distribution, so to speak, is the Binomial Distribution Without Q. * * * The Poisson Distribution, as a data set or as the corresponding curve, is always skewed toward the right, but it is inhibited by the Zero occurrence barrier on the left. The degree of skew diminishes as r becomes larger, and at some point the Poisson Distribution becomes, to the eye, about as symmetrical as the Normal Distribution.

* The UMass paper does not label x and y axes in the top graph. For that see
en.wikipedia.org/wiki/Poisson_distribution
, where the top graph shows λ (OR r, meaning “rate”) = 4 (4 letters OR murders a day) and whose legend reads, “The horizontal axis is the index k, the number of occurrences. The function is only defined at integer values of k. The connecting lines are only guides for the eye.”  The last two sentences means “k, the number of occurrences” can not be  ½ or 0.3 (must be an “integer”).  What the legend does not say is that y axis is probability (“p” or “pr” for short: “p” is used in UMass paper and “pr” used in this Wikipedia page). Following the curve of λ (or r) = 4, you know the probability (y axis) of getting 1 or 5 letters a day.
* The “p” and “q” in the second quotation is probability for each of the binomial distribution (events P (head) and Q (tail); think tossing a coin which may or may not be unbiased).
* You have to read the UMass paper yourself, which colors (rather than Italicize) the emphasis in the quotations.


(d) “To this end, the book alternates traditional passages of statistical exposition with little parables about three characters: risk-averse Prudence, daredevil Kelvin and the protagonist of the book, Norm himself, who lands squarely on the median of every statistical category used to slice and dice the UK population. You know how they say the average person has 2.8 household accidents a week? Norm is that person.”
(i) Norm is the short form of given name Norman
en.wikipedia.org/wiki/Norman_%28name%29
(section 1 Etymology; section 1.2 Given name)
(ii) norm (n; Latin norma, literally, carpenter's square)
www.merriam-webster.com/dictionary/norm
(definition 3)