tag:blogger.com,1999:blog-9430835.post5748954675133582488..comments2021-05-15T22:54:25.218-07:00Comments on Steve Sailer: iSteve: Calling all actuariesUnknownnoreply@blogger.comBlogger51125tag:blogger.com,1999:blog-9430835.post-37378105925062102072009-08-07T07:09:33.463-07:002009-08-07T07:09:33.463-07:00I didn't try to wade through all of the respon...I didn't try to wade through all of the responses but here is an answer to the wife vs. husband life expectancy question as supplied by my friend the actuary (BTW, for what it is worth, this guy is an actuaries actuary who knows his stuff in spades):<br /><br /><i>Oh, ok. Here's a general idea of how to calculate the odds that wife will die first, only slightly simplified. You break it up into pieces, or individiual years, then add up the totals. We have estimated probabilities of death for each person for each age from their current ages and the rest of their lives. Calculate the chance that wife will next in the next year and husband will live. Put that aside. Calculate the chance that both of them will survive the next year, but wife will die in the following year and husband will survive. Put that aside. Calculate the chance that both of them will survive the next 2 years, but wife will die in the following year and husband will survive. Put that aside. You keep going until the probabilities of survival are so small that they are negligible. Then you add up all the "Put that asides" This ignores the case where both of them die in the same year, but that's just a refinement. Now that I think about it, maybe this is good enough for Steve Sailer, so send it to him if you like."</i>spacehabitatshttps://www.blogger.com/profile/01540280499274649411noreply@blogger.comtag:blogger.com,1999:blog-9430835.post-44937226713684202752009-08-06T15:47:00.548-07:002009-08-06T15:47:00.548-07:00A few years ago in Berkeley I ran into a black guy...A few years ago in Berkeley I ran into a black guy I'd played basketball with regularly in the 90's. He said, "I'm surprised you're still alive." He was referring to my habit of speaking to black guys sans the usual deference.hot a hackernoreply@blogger.comtag:blogger.com,1999:blog-9430835.post-52824140801424780412009-08-06T07:21:25.133-07:002009-08-06T07:21:25.133-07:00In something close to actuarial notation:
sum[y:6...In something close to actuarial notation:<br /><br />sum[y:62 to 100] qm[y] pw[y-62+55] <br /><br />qm[y] is prob man lives to age y and dies by age y+1<br /><br />pw[z] is prob woman lives after age z = y-62+55+1<br /><br />You can replace 100 by max age man.Old Atlantic Lighthousehttps://www.blogger.com/profile/11851308758539648628noreply@blogger.comtag:blogger.com,1999:blog-9430835.post-13395297538791223042009-08-06T07:04:03.605-07:002009-08-06T07:04:03.605-07:00Man age 62. Wife age 55. Assume max age for man ...Man age 62. Wife age 55. Assume max age for man is 100.<br /><br />Sum over y from 62 to 100:<br /><br />probability man lives to age y and dies by age y+1<br />* prob wife lives after age <br />55+ (y-62)+1.<br /><br />This still is an approximation but is close enough for now.<br /><br />To get probability to die between year y and y+1 for a man from a table of prob to survive after age y, take difference of each succeeding element of prior element. If you can find the data in a csv format you can download it and do the calculations.Old Atlantic Lighthousehttps://www.blogger.com/profile/11851308758539648628noreply@blogger.comtag:blogger.com,1999:blog-9430835.post-41842030500758003322009-08-05T17:39:29.256-07:002009-08-05T17:39:29.256-07:00"I.e. if you have the choice between being tr..."I.e. if you have the choice between being treated for a medical condition in a socialized medicine country versus fleeing to [what's left of] free-market capitalistic medicine in the good ol' US of A, then it pays to flee as fast as your feet will take you."<br /><br />Rich Japanese fly to the USA for treatment for anything complicated. The Japanese system is good at prevention and care for small things but terrible at treatment of serious illnesses. That is one of the conundrums of socialized medicine vs the US system.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-9430835.post-70334064369404031452009-08-05T17:38:40.293-07:002009-08-05T17:38:40.293-07:00I am the one who posed the question to Steve, so I...I am the one who posed the question to Steve, so I'll begin by thanking all of you above for your kind suggestions. Some were over my head, so maybe they are better than my own idea as follows:<br /><br />I looked at the CDC website and found the life expectancy for a white male of my age (62). Using another table at that site I calculated the percent of white females of my wife's age (55) expected to live beyond the span given for me (20). As the result seemed intuitively plausible I accepted it. It looks as though there is a 78% probability that she'll be there to put a flower on my grave and only a 22% probability I'll be burying her - a fringe benefit of marrying a woman seven years younger.<br /><br />BUT if you experts think I've gone about this all wrong, please blast away. (Comments that I should have married an even younger woman will be deemed hostile.)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-9430835.post-21314808559811854852009-08-05T17:24:21.443-07:002009-08-05T17:24:21.443-07:00If you're a White American male be/live near S...If you're a White American male be/live near Scandinavians, Canadians and/or Jews. In a pinch, Aleuts, Polynesians or (gasp) Hispanics will do.<br /><br />Maybe the 'always fighting' Scots-Irish are doing too much always fighting?<br /><br />Gold dust not coal dust?<br /><br />Violins not fiddles?<br /><br />Ha-Ha not Hee-Haw?anony-mousenoreply@blogger.comtag:blogger.com,1999:blog-9430835.post-46580965443757573092009-08-05T15:30:51.799-07:002009-08-05T15:30:51.799-07:00Oh, and feel free to unlock my spreadsheet to see ...Oh, and feel free to unlock my spreadsheet to see how I did the calculations.meephttps://www.blogger.com/profile/08893035949118989768noreply@blogger.comtag:blogger.com,1999:blog-9430835.post-92039877900573051982009-08-05T14:38:20.954-07:002009-08-05T14:38:20.954-07:00If actuarial data are available, I dont see the ne...If actuarial data are available, I dont see the need for messing around with theoretical distributions at all. One must simply be willing to apply the truncated male and female life expectancy distribution (from the present age of husband and wife respectively) and calculate the dominance of the wife distribution over the husband distribution (assuming wife is younger). The calculations require nothing more than simple algebra and perhaps excel/spss (it is functionally the equivalent of the double integral for 2 continuous overlapping normal or other distributions that others are talking about here) which I made in a post here (but it hasnt appeared yet).nsamnoreply@blogger.comtag:blogger.com,1999:blog-9430835.post-65443215645746955052009-08-05T14:21:11.786-07:002009-08-05T14:21:11.786-07:00The question of finding the probability of the wif...<i>The question of finding the probability of the wife outliving the husband doesn't seem to have a simple answer.</i><br /><br />Yes, because you're talking about taking two curves (or the tails of two curves) and then doing subtraction(s) of their area (and then looking at a ratio). You can't do it without integrating, and any formula is going to be an approximation as the curves don't follow a simple mathematical shape. For example neither the poisson nor the normal distribution is applicable.bbartlognoreply@blogger.comtag:blogger.com,1999:blog-9430835.post-54246762719876448552009-08-05T13:37:25.022-07:002009-08-05T13:37:25.022-07:00Blessings you deserve for the confession of your &...Blessings you deserve for the confession of your "sin" of ignorance re life expectancy, something I don't understand either. Everyone's ignorant of something, but most prefer to feign omniscience. <br /><br />Nietzsche dreamed of a culture where young intellectuals were taught: "above all, do not <i>pretend!</i>"<br /><br />I had a history prof for a grad/undergrad course - a good man who I otherwise wanted to like - who told us to "fake it til you make it." What <i>possible</i> defense of this could there be?blue anonymousnoreply@blogger.comtag:blogger.com,1999:blog-9430835.post-13381169410800295862009-08-05T13:10:56.030-07:002009-08-05T13:10:56.030-07:00The question of finding the probability of the wif...The question of finding the probability of the wife outliving the husband doesn't seem to have a simple answer. This link gives an integral that is equal to this probablility:<br /><br />http://books.google.ca/books?id=ny2MJU4A3DIC&pg=PA467&lpg=PA467&dq=how+to+find+probability+that+husband+lives+longer+than+wife&source=bl&ots=NkI0yfe4xw&sig=IjyxuUhhHhTSfjcYfZXphDi1ePA&hl=en&ei=BeZ5SruuLJCoswOAs8jlBA&sa=X&oi=book_result&ct=result&resnum=2#v=onepage&q=&f=false<br /><br />The functions are defined on the previous (page 466). Sorry it is such a long URL.Melykinnoreply@blogger.comtag:blogger.com,1999:blog-9430835.post-87388838056912161522009-08-05T12:15:02.792-07:002009-08-05T12:15:02.792-07:00I can help.
Life expectancy is just the average t...I can help.<br /><br />Life expectancy is just the average time of death of a population, whatever that population is defined as. So regional life expectancy would only take into account where each person dies, not how long they have lived there or where they came from.<br /><br />As for your reader's question: <br /><br />First he needs to determine the probability distribution of time of death random variable he is going to use.<br /><br />He could use a normal distribution, or a uniform distribution (De Moivre's law), but it would probably be easiest to use use an exponential distribution. <br /><br />Here are the variables:<br /><br />X = time of death of the man.<br />Y = time of death of female.<br />E[X] = life expectancy of man.<br />E[Y] = life expectancy of female. <br /><br />Here is the algorithm:<br /><br />The joint probability density function is going to be (using Excel notation)....<br /><br />f(X,Y) = EXP[-(X/E[X] + Y/E[Y])]/(E[X]*E[Y])<br /><br />All that needs to be done at this point is a double integral over the probability space where Y is greater then X. I would integrate the density function in this order, with these arguments:<br /><br />1) X from 0 to Y<br />2) Y from zero to infinity<br /><br />This method assumes independent lives but given the information available it is a pretty good assumption. Anyway, hopefully that helpful in addressing any of your questions.stephennoreply@blogger.comtag:blogger.com,1999:blog-9430835.post-16638367752166424312009-08-05T11:13:20.830-07:002009-08-05T11:13:20.830-07:00The relevant technique is something called cohort ...The relevant technique is something called cohort survival. It requires a bit of matrix algebra. I studied it in grad school but never used it professionally. I taught statistics for several years but never taught matrix manipulations. <br /><br />All of which is to explain (excuse ?) the fact that although I know it's the appropriate technique, I can't for the life of me remember how it works.albertosaurushttps://www.blogger.com/profile/13209465319904999278noreply@blogger.comtag:blogger.com,1999:blog-9430835.post-76112455969835263832009-08-05T10:26:47.363-07:002009-08-05T10:26:47.363-07:00http://en.wikipedia.org/wiki/Actuarial_notation
j...http://en.wikipedia.org/wiki/Actuarial_notation<br /><br />joint life contingency:<br /><br />http://www.utstat.utoronto.ca/~sheldon/Exam-M-temp.pdf<br /><br /><br />http://www.business.uiuc.edu/ormir/JRI%20Dec%202000.pdf<br /><br />Search on: joint life expectancy table.Old Atlantic Lighthousehttps://www.blogger.com/profile/11851308758539648628noreply@blogger.comtag:blogger.com,1999:blog-9430835.post-56190556514390415162009-08-05T10:15:08.929-07:002009-08-05T10:15:08.929-07:00Take the death rate for the relevant group at each...Take the death rate for the relevant group at each age, assume it remains constant forever, and calculate the expected value of the lifespan of a person born today. You can also use a recursive formula -- life expectancy of an N-year-old today is approximately (p+((1-p)/2))*(1+X) where X is the life expectancy of an (N+1)-year-old today and p is the probability that an N-year old will survive the next year. (The (1-p)/2 term is because even the ones who won't survive the year will live an average of 6 months more.)Polymathhttps://www.blogger.com/profile/12332963337386407840noreply@blogger.comtag:blogger.com,1999:blog-9430835.post-73240522631829728652009-08-05T10:03:09.746-07:002009-08-05T10:03:09.746-07:00I'll assume you have a mean and variance for b...I'll assume you have a mean and variance for both your age at death and hers. Assuming gaussian distributions for both, the joint distribution is bivariate normal (a 2-d gaussian). Integrate this distribution over the region above (or below) the line x=y. That's the probability you (or she) will outlive the other.<br /><br />And it's only technically incorrect to consider the probability of a single event if you took statistics from a math professor. Most other fields which use probability have moved past this non-issue.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-9430835.post-60769160087233766172009-08-05T09:48:17.896-07:002009-08-05T09:48:17.896-07:00The reader might want to compare the life spans of...The reader might want to compare the life spans of his parents to that of his wife's parents for more data to predict his vs. hers lifespan. Long-livedness does tend to run in families. But of course anything can happen in any one individual case.StephenTnoreply@blogger.comtag:blogger.com,1999:blog-9430835.post-4958521993319271342009-08-05T09:26:34.949-07:002009-08-05T09:26:34.949-07:00I am an actuary. Life expectancies are based on so...I am an actuary. Life expectancies are based on something called mortality tables, which are tabulated probabilities of dying between your last and your next birthday at any given age. These tables are calculated for various segments of population. A whole bunch of them can be downloaded from here: http://www.soa.org/professional-interests/technology/tech-table-manager.aspx<br /><br />The life expectancy at a given age, say 50, is the probability of surviving to your 51st birthday, plus the probability of surviving to your 52nd birthday, and so on. When they say simply "life expectancy" without mentioning the age they usually mean life expectancy at birth, i.e. age zero. <br /><br />If two counties in your example are governed by the same mortality table, their life expectancy would be the identical, no matter the age distribution.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-9430835.post-28204623003600174852009-08-05T09:19:52.941-07:002009-08-05T09:19:52.941-07:00Social Security Administration publishes tables of...Social Security Administration publishes tables of life expectancy at different ages. So you can see life expectancy for people who have already reached a certain age.<br /><br />http://www.ssa.gov/OACT/STATS/table4c6.html<br /><br /><br />Similar tables can be found elsewhere as well.read ithttps://www.blogger.com/profile/00631238731651674916noreply@blogger.comtag:blogger.com,1999:blog-9430835.post-89172788576318493962009-08-05T09:06:37.711-07:002009-08-05T09:06:37.711-07:00Life expectancy stuff is often annoying. For exam...Life expectancy stuff is often annoying. For example, speaking colloquially, people often say,"Life expectancy in 18th century England was 37," or even "The average person in 18th century England was dead at 37," or some such thing, but if you read 18th century books or books written about the 18th century, you see there are lots and lots of old people running around. The high infant and child mortality rate of the 18th century lowers the average for everybody, but if an 18th century European makes it to his teens, he will likely live about as long as a 20th century European.<br /><br />http://www.psychologytoday.com/blog/the-scientific-fundamentalist/200811/common-misconceptions-about-science-ii-life-expectancyAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-9430835.post-31884272885562945582009-08-05T08:47:21.298-07:002009-08-05T08:47:21.298-07:00I think life expectancy means something like the f...I think life expectancy means something like the following.<br /><br />In a large population, you see what fraction of those who turn, say, 47 are still alive to turn 48.<br />That observed fraction is defined to be the probability of survival from the 47th birthday until the 48th birthday for a person in that population. Likewise for other ages.<br /><br />The probability of death at age 59 for a newborn is then calculated by multiplying all the survival probabilities for ages 0, 1, 2, ...,58 times the non-survival probability for age 59.<br /><br />Life expectancy (for that population) would them be the average age of death for those calculated probabilities for age of death.<br /><br />So, if in two populations, the fraction dying is the same for both populations at every age, the life expectancies would be equal, even if the age distributions are not equal.<br /><br />Real actuaries may do something a bit more refined, but I'm pretty sure that's the basic idea.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-9430835.post-17490753659088090072009-08-05T08:21:04.980-07:002009-08-05T08:21:04.980-07:00Steve, I noticed that you have never written about...Steve, I noticed that you have never written about the Singularity, which will supposedly lead to radical life-extension. Theoretically, it is possible; however, I am not as optimistic as some (it may take more than 34-40 years).Shawnnoreply@blogger.comtag:blogger.com,1999:blog-9430835.post-63024170320971299992009-08-05T08:08:22.291-07:002009-08-05T08:08:22.291-07:00I'm no expert here, but I've always wonder...I'm no expert here, but I've always wondered about the robustness of these data. For example, I once lived in a large city with a fair number of hospitals. Using Medicare data, the feds published the crude mortality rates for all the hospitals. One hospital stood out as much higher than all the others. I happened to have staff privileges at that hospital and knew it to be very high quality. It turned out that this hospital had the city's only hospice unit, and all the hospice deaths were rolled into the hospital's numbers. The hospital was outraged and called on the feds to redo the numbers, but they seemed baffled by the whole thing and, of course, did nothing. So the hospital paid a private firm to recalculate the mortality data and found that its death rate was actually lower that the city average. I wonder how much of this stuff really goes on?Nednoreply@blogger.comtag:blogger.com,1999:blog-9430835.post-30100083913284806322009-08-05T07:27:32.384-07:002009-08-05T07:27:32.384-07:00A little off-topic, but I have been told that if y...A little off-topic, but I have been told that if you throw out African-Americans and Aboriginal Hispanics, then e.g. the [normal old-fashioned blue-blooded Caucasian] American survival rate for cancer just dwarfs that of the average European [or Canadian or Japanese or Korean or anyone else].<br /><br />I.e. if you have the choice between being treated for a medical condition in a socialized medicine country versus fleeing to [what's left of] free-market capitalistic medicine in the good ol' US of A, then it pays to flee as fast as your feet will take you.<br /><br />[But don't worry, Rahm & David & Chuckie and Barnie will see to it that we lose even that most meager of luxuries.]Posting Anonymouslynoreply@blogger.com