Post by Anthony William Sloman<snip>
Post by Anthony William SlomanPost by Fred BloggsPost by Anthony William SlomanYears ago it was claimed that males who survived past 80 in good health and women who survived past 85 in good health were predominantly drawn from that more robust population.
It's a statistician's play ground. In practical terms you can't work out precisely what population you belong to - you might just be a lucky snowflake.
An Australian male has an average life expectancy of 81.2 years, so at 81 and a couple of months I might be expected to drop dead soon. As an Australian male of 81, I've actually As an Australian male of 81, I've actually got a life expectancy of 8.44 more years.
In reality, as an 81-year-old Australian male who never smoked and managed to get a Ph.D. I'm a member of an even longer-lived cohort, but they don't split the life expectation table finely enough that I can quote a number.
Post by Fred BloggsNot really. That life statistic has a standard deviation to it. I don't know what it is for males age 72-88, but for the general population, it is 8 years. That would be 8 years either side of the mean. 2/3 of people die with a standard deviation of the mean. So that would be 33% in the range mean + 8 years. That's not called dropping dead soon.
As usual, you managed to insert you comment in the middle of my paragraph,
The expectation of life at a given age does tend to shrink as you get older, and the standard deviation can be expected to shrink in proportion. Your assertion assumes that the subsequent life spans will be normally distributed, and they won't be.
I'm not much of a statistician, but you even worse informed.
Your idea of being informed is a self-delusion.
Perhaps, but I'm clearly better-informed than you are.
Of course you're going to think that, it's an ego preservation refuge for the megalomaniac.
Post by Anthony William SlomanThe density function for years of life should be normal-like, a crude fit is said to be the log-normal, the logarithm of an underlying normal variate. Literature is calling it a survival distribution, which makes sense. If F(A) is the cumulative distribution (integrated ) of that density up to year A, indicating the fraction of population still alive by year A. Then the chance of an individual of age A living to age A + T, T being time interval of continued life, should be F( A + T)- F( A ). What you're after, whether you realize it or not is the distribution of T. Literature says it's an exponential distribution, and that makes no sense at all since it implies a constant death rate. If you can't compute the mean and standard deviation of that simple thing, then you have problems.
A rather long-winded way of announcing that you don't know what you are talking about.
I know exactly what I'm talking about. The fact of you saying it's long winded goes to show how weak is your so-called analytical thinking.
Post by Anthony William Slomanhttps://users.stat.ufl.edu/~rrandles/sta4930/4930lectures/chapter2/chapter2R.pdf
They think they're geniuses for fitting a Weibull.
It's a shopping list of fitting functions. There's nothing in that write-up that shows the fit of an actual function to actual acturial data.
It's a parameterized distribution used for fitting exponentials, and used extensively in modeling systems for reliability engineering lifetime statistics, just something else you don't know the first thing about.
Post by Anthony William Slomanhttps://en.wikipedia.org/wiki/Survival_function
That is marginally better, in that it makes passing reference to real world breast cancer data, but it doesn't make any direct connection.
Statistics is a tool of scientific discovery and not the science itself. Dunno what kind of childish arrested development would think it would be.
Post by Anthony William SlomanYou do go to a lot of trouble to tell us that you don't know what you are talking about.
You're too ignorant with an exacerbation of stupidity to make that assessment.
Post by Anthony William SlomanThe improved survival past age 80 for males and 85 for females might be susceptible to being modelled by a Weibull function - I wouldn't know. I could ask my cousin the statistician, but even though he is retired, I'd hate to waste his time on such a pointless question.
It's more than just a model. It does show that beyond a critical age range the death rate becomes constant, being directly proportional to the interval of time under consideration regardless of when that interval occurs, up to a limiting age when it rapidly breaks down.
You're too much of lightweight to understand any of that, so go ahead and call bullshit- the refrain of ignoramuses.
:
The exponential distribution is often concerned with the amount of time until some specific event occurs. For example, the amount of time (beginning now) until an earthquake occurs has an exponential distribution. Other examples include the length of time, in minutes, of long distance business telephone calls, and the amount of time, in months, a car battery lasts. It can be shown, too, that the value of the change that you have in your pocket or purse approximately follows an exponential distribution.
Values for an exponential random variable occur in the following way. There are fewer large values and more small values. For example, marketing studies have shown that the amount of money customers spend in one trip to the supermarket follows an exponential distribution. There are more people who spend small amounts of money and fewer people who spend large amounts of money.
Exponential distributions are commonly used in calculations of product reliability, or the length of time a product lasts.
The random variable for the exponential distribution is continuous and often measures a passage of time, although it can be used in other applications. Typical questions may be, “what is the probability that some event will occur within the next x
hours or days, or what is the probability that some event will occur between x1
hours and x2
hours, or what is the probability that the event will take more than x1
hours to perform?” In short, the random variable X equals (a) the time between events or (b) the passage of time to complete an action, e.g. wait on a customer. The probability density function is given by:
f(x)=1μe−1μx
where μ is the historical average waiting time.
and has a mean and standard deviation of 1/μ.
An alternative form of the exponential distribution formula recognizes what is often called the decay factor. The decay factor simply measures how rapidly the probability of an event declines as the random variable X increases.
When the notation using the decay parameter m is used, the probability density function is presented as:
f(x) = me−mx
where m=1μ
In order to calculate probabilities for specific probability density functions, the cumulative density function is used. The cumulative density function (cdf) is simply the integral of the pdf and is:
F(x)=∫∞0[1μe−xμ]=1−e−xμ '
:
Total waste of time to post that, you and numbers don't get along.
https://openstax.org/books/introductory-business-statistics/pages/5-3-the-exponential-distribution
I'm finding the business pages have the best explanations for statistical principles. They do the best job of making real sense of it. The 'nurd' pages are mostly jackass-inine factoid regurgitators. The nurds are used to being confused.