Quantitatively Yours

2011-04-28T00:36:00.000-07:00

In his article "Optimum Strategies for Creativity and Longevity" Dr. Sing Lin gives an interesting actuarial table of Retirement Age and Age at Death which is reproduced below:

Retirement Age		Age at Death
49.9		86
51.2		85.3
52.5		84.6
53.8		83.9
55.1		83.2
56.4		82.5
57.2		81.4
58.3		80
59.2		78.5
60.1		76.8
61		74.5
62.1		71.8
63.1		69.3
64.1		67.9
65.2		66.8

A quadratic regression model can be nicely fitted to this data:

Age of Death = - 121.2 + 8.335 Retirement Age - 0.08394 Retirement Age**2

S = 0.713363 R-Sq = 99.0% R-Sq(adj) = 98.8%

It seems that one should plan to retire by 58 or 60 to benefit from the fruits of his /her hard work.

Odds for ICC World Cup Win

2011-03-31T09:43:00.000-07:00

I found the following at this site : http://www.cricket-worldcup.net/finals.html

=================================

India v Sri Lanka Win Betting - 02/04/11

Sri Lanka v India - 02/03/11

India are 4/6 to win, Sri Lanka are 6/5 to win with Boylesports

=========================================

If converted to probability this means that probability of India winning is 0.4 and that for Sri Lanka winning is 0.545. It is interesting to observe that these two probabilities do not add up to 1.

Suppose now the betting house sells one bet of $100 for India winning to A and another bet of $100 on Sri Lanka winning to B.

Then in case India wins the betting house returns $100 (to A) and pays out $150 additional (to A). It keeps $100 of B. So the net loss for the house is $50.

In case SriLanka wins the betting house returns $100 (to B) and pays out $83.33 (to B). It keeps $100 of A. So the net gain for the house is $16.77

How is the betting house going to make money then? The answer possibly is that it expects lot more gamblers to bet on Sri Lanka winning than on India winning. This can be explained from prospect theory. Since, the chance of Sri Lanka winning is more than that of India winning, for a gambler the chance of losing $100 is more when betting for India than for Sri Lanka. This will drive a larger number of gamblers to bet for Sri Lanka. The fact that they (gamblers) stand to gain about 80% more if they win by betting for India than for Sri Lanka is likely to be overridden by the fact that the chance of losing of $100 is 32% more when betting for India than for Sri Lanka.

An interesting illustration of Prospect Theory is practice !!!

Will Sensex hit 21000 before Diwali?

2010-10-31T09:44:00.000-07:00

I saw a news item in a newspaper website speculating that the Sensex will cross 21000 prior to Diwali. As per my calculations the chance is not that bright. It is only about 9%.

Here is the probability distribution of the value of Sensex on the pre-Diwali day:

Less than 19000 - 5%

Between 19000 to 19500 - 14%

Between 19500 - 20000 - 28%

Between 20000 - 20500 - 26%

Between 20500 - 21000 - 18%

Above 21000 - 9%

Happy Diwali!

Octopus Paul - Psychic Forecaster

2010-07-09T12:00:00.000-07:00

It is amazing to see how chance can fool us!!! Look at the worldwide craze about octopus Paul. The eight legged creature got six successive predictions about Germany's games correct and is being heralded as a "psychic forecaster". Nobody (especially the journalists) seems to be asking the simple question - How often will that happen just at random? The answer is also easy to compute. The Octopus's prediction can be thought of as a string of heads and tails obtained from tosses of a fair coin. The probability that the string generated by the octopus matches the actual string is

= (1/ 2^6)= 1/64 = 0.015. That is the chance is about 1.5%. What we have seen is an occurrence of a low probability event and we are immediately driven to see a pattern!!! Fooled by Randomness!

How low can Sensex go this month?

2009-11-03T10:44:00.000-08:00

The sudden fall in the BSE-Sensex has disturbed many a investor and the question foremost in their mind is: How low can this get? I try to answer this question quantitatively below.

Here are my predictions for the lowest value of Sensex for the period 4-Nov to 30-Nov.

Chance of Sensex closing below 15000 on someday within this period: 58%

Chance of Sensex closing below 14000 on someday within this period: 14%

Chance of Sensex closing below 13000 on someday within this period: 2%

Another question that investors are interested in are the chances of an upswing. The chances of these positive happenings are given below:

Chance of Sensex closing above 16000 on someday within this period: 55%

Chance of Sensex closing above 17000 on someday within this period: 17%

Chance of Sensex closing above 18000 on someday within this period: 4%

On NIFTY-2

2009-10-01T11:25:00.000-07:00

Here are my predictions of the possible closing value of NIFTY for the next week:

Date P5 Q1 Med Q3 P95

5-Oct 4921 5042 5089 5136 5226

6-Oct 4870 5015 5093 5165 5291

7-Oct 4830 5003 5099 5190 5341

8-Oct 4795 4990 5104 5216 5394

9-Oct 4772 4980 5111 5234 5438

P5 = 5th percentile

Q1 = 25th percentile

Med = 50th percentile

Q3 = 75th percentile

P95 = 95th percentile

On NIFTY - 1

2009-09-14T11:40:00.000-07:00

There is now a lot of speculation regarding whether NIFTY will cross 5000 or not. As per my calculations

(a) the chance that the closing value of NIFTY on 1-Oct-2009 will exceed 5000 is 33.5% and

(b) the chance that the closing value of NIFTY on 16-Oct-2009 will exceed 5000 is 41.7%

Deaths due to Swine Flu in India - Predictions for Sept 11 -15

2009-09-10T12:21:00.000-07:00

The prediction of the number of deaths due to swine flu for the next five days is:

Date Forecast 95% Prediction Interval

11-Sep 154 (150, 158)

12-Sep 159 (155, 164)

13-Sep 164 (159, 169)

14-Sep 170 (164, 175)

15-Sep 175 (169, 181)

(The analysis is based on data available from http://www.swineflu-india.org/)

Y-o-Y quarterly GDP growth of India (2009-10)

2009-09-05T12:11:00.000-07:00

Based on the data on Year-on-Year (Y-o-Y) quarterly growth of GDP (at constant 1999-2000 prices) over the period 1997-98 to 2008-09 my predictions for the Y-o-Y quarterly growth for 2009-10 (at constant 1999-2000 prices) are as follows:

Forecast (%) 95% prediction interval

Q1 6.0 (3.1, 8.9)

Q2 6.9 (3.1, 10.7)

Q3 7.2 (3.0, 11.5)

Q4 7.8 (3.2, 12.4)

Swine Flu in India - 8

2009-09-05T10:36:00.000-07:00

My forecasts for the number of deaths due to swine-flu for the next five days are as follows

Date Forecast 95% prediction interval

6-Sep 126 (123, 129)

7-Sep 131 (128, 134)

8-Sep 136 (132, 139)

9-Sep 141 (137, 144)

10-Sep 145 (142, 149)

The data on the statewise mortality figures given in http://www.swineflu-india.org/ continues to show remarkable heterogenity in the apparent mortality rate. Gujarat has the highest apparent mortality rate (~9%), followed by Karanataka (~6%). In contrast Delhi has an apparent mortality of 0.4% while the same for Tamil Nadu is 0.6%.

Swine Flu in India - 7

2009-09-01T11:50:00.000-07:00

Here are my predictions of the cumulative number of deaths in the period 1-Sep to 5-Sep. These are based on the available data on the cumulative number of deaths between (21-Aug to 31-Aug).

Date Forecast 95% Prediction Interval

1-Sep 103 (101, 106)

2-Sep 108 (106, 111)

3-Sep 113 (111, 116)

4-Sep 118 (116, 121)

5-Sep 123 (121, 126)

There had been 37 reported deaths due to swine flu during the week 25-Aug to 31- Aug. This is almost equal to 38 deaths reported in the week 18-Aug to 24-Aug. From the predictions it appears that we will have similar number of deaths in the coming week.

The number of confirmed positive swine-flu cases in the period 25-Aug to 31 - Aug was 1077 and that for the period 18-Aug to 24-Aug is 982.

Swine-flu in India - 6

2009-08-31T00:55:00.000-07:00

A study of the apparent death rates due to swine-flu for various states of India indicates that Gujarat has the highest rate of about 8% while Delhi has the lowest of about 0.5%. In terms of laboratory confirmed swine-flu cases Gujarat has only about 2.5% compared to about 17% of Delhi. Even in Maharashtra which has about 41% of the total confirmed swine-flu cases the death rate is only about 3.2% which though substantially higher than that of Delhi is also substantially lower than that of Gujarat. It is also interesting to see the difference in the apparent death rates of the two neighbouring states Tamil Nadu and Karnataka. While Tamil Nadu has a death rate of about 0.8% the same for Karnataka is about 5.6%. It is to be noted that both these states has similar number of confirmed cases (Tamil Nadu - 9.3%, Karnataka - 11.1%). I feel the differences in the death rates may be either due to large number of undiagnosed swine-flu cases in some states or may be due late treatment allowing onset of complications. Which one is the correct cause?

On Swine flu in India - 5

2009-08-27T10:31:00.000-07:00

My projections for laboratory confirmed total number of cases and new cases (based on data from 19-Jul to 26-Aug) is as follows

Date New Cases Total 95% prediction interval for Total

28 Aug 201 3664 (3443, 3899)

29 Aug 213 3877 (3572, 4208)

30 Aug 225 4102 (3705, 4543)

31 Aug 239 4341 (3841, 4906)

My projections on the cumulative number of deaths predicted on the above days are:

Date Total 95% prediction interval of no. of total deaths

28 Aug 84 (78, 89)

29 Aug 90 (84, 96)

30 Aug 96 (90, 102)

31 Aug 103 (97, 109)

On Swine flu in India - 4

2009-08-25T11:53:00.000-07:00

How many persons would an swine-flu infected person who is undiagnosed going to infect on the average? While no exact answer can be given based on available data one can reasonably conclude that this number would be between 2 and 2.7. Since it takes about a week from infection to development of symptoms the above fact implies that the total number of infections would more than double every week unless immediate steps are taken to slow down the spread of infection.

There had been 38 deaths in the week 18-24 August and it is quite likely that the total number of deaths would more than double in the week 25-31 August. The doctors and the public health experts need to intervene more aggresively with new policy measures to prevent a major public health catastrophe.

On Swine flu in India - 3

2009-08-24T11:51:00.000-07:00

What is the estimated number of cases in India till date? Is it 2909 as reported by media? The answer ofcourse is NO as I had suggested in my last blog looking at the apparent mortality rate data. On 9th August 2009 the apparent mortality rate was about 0.5% which is the rate that is widely held to be the correct number. The present apparent mortality rate is about 2.2%. This indicates that a large number are cases are not laboratory confirmed. A simple calculation indicates that there has been around 12600 cases of swine flu in India of which more than 9000 are not laboratory confirmed cases? The fundamental questions that arises are:

Q1: Did these people infect others? This is quite likely given the contagious nature of the infection

Q2: Did these people receive any treatment? Surely not all.

In the last week I estimate that around 7600 new cases of swine flu has occurred of which only 982 has been laboratory confirmed while in the previous week only around 3800 new cases occurred of which 968 were laboratory confirmed cases. This gives an indication that the number of new swine flu cases is possibly doubling every week. The next week is likely to have more than 15000 cases and around 75 deaths.

The government should reconsider its strategy of dealing with this problem. It may be prudent to make the drug Oseltamivir available through retail pharmacies so that the patients who need it can quickly access the drug. Also, the government may more actively train some of the good private laboratories to do this test so that doctors can access these laboratories when needed and unnecessary deaths due to delay in treatment can be avoided.

On Swine flu - 2

2009-08-23T05:20:00.000-07:00

Only about 19% of the samples tested for swine-flu has returned positive. This is of course expected since the clinical markers for suspecting swine-flu is not very different from that of common flu. Since the diagnostic test facilities are not many and the test is quite expensive it may be worthwhile for the public health authorities to spend some money on research for better (preliminary) indication of swine flu. I anticipate it would not be hard to come up with a system based on bayesian methods that can give substantially better indication. This system can possibly be also deployed over the internet.

Swine Flu Progress in India - 1

2009-08-22T12:00:00.000-07:00

The projected number of laboratory confirmed swine-flu cases in India in the next five days based on my calculations are as follows:

New Cases Total

23 Aug 142 2812

24 Aug 144 2956

25 Aug 150 3106

26 Aug 155 3261

27 Aug 161 3422

The apparent mortality rate =(total no. of deaths/total no. of cases) appears to be quite large for India (about 2%) compared to the rest of the world. This can be due to under estimation of the denominator since a large number of swine flu cases may not be referred for testing at a designated centre.

If we assume that the widely reported 0.5% mortality rate is also true for India it indicates that the actual number of cases can be about the four times the laboratory confirmed numbers.

Since nearly three-fourths of the cases of swine-flu are not detected these individuals will spread the disease without their knowing. This can be a cause of concern particularly for the high risk groups.