Statistics question

[hhiusa]

I have taken a sample population of a population with unknown size. The sample size is 54 trades. The sample mean is 2.1% (1.021) return per trade. The sample standard deviation is 0.01. 100% of the 54 trades were profitable i.e., X>1.00. I wish to know with a certain confidence, how close the sample mean and standard deviation are to the population mean and standard deviation. I would also like to know what is the probability of the 55th trade and subsequent trades being >1.00.

Z-score = 0.021/0.01 = 2.1

Z from the cumulative normal distribution function

The extrema should then be the greatest standard deviation with the lowest mean and the lowest standard deviation with the highest mean.

Does this mean that I am 95% confident that 91.8% of future trades will be profitable or that the 55th trade will be profitable. Does this also mean that at that exact point in time the worst case scenario is 91.8%.

 

[Forexmospherian]

This statistical question you have raised hhiusa is pure mathematical and so its real meaning in the real world is of limited use.

My question back to you would therefore be .............Why ?

You mention that 100% of the sample - ie 54 trades - were profitable.

OK - so then go on to show that the Z score is 2.1 and positive

So the probability is very high

Ok in the real world the 55th trade could still fail - and that is the most important part of what you need to know

Whether you are 95% confident that 91.8% of all future trades will be profitable or not is of NO significance in the real world to you saying you are only 86% confident of 94.2% of all future trades will be profitable.

Personally - I reckon you need a larger sample - ie >100+ or even better >1000

Otherwise stick 3 Maths Professors in a room together - and I bet one would disagree with the other 2 and would be able to explain with another formula that the assumption you have made are incorrect

Last point

What ever you do - dont ask any American Maths Professors - stick with reliable European ones - Harvard and MIT students are not the World's best - as I am sure you want to prove next ;-))

Look forward to your next thread with 99.9% enthusiasm - make sure its a good one




Regards


F

 

[NVP]

if statistics worked all the time then all academics would be millionaires from their investments and trading endeavours

they are not ..........
N

 

[NVP]

HH

really enjoying your energy here at T2win................enjoying the banter !

N

 

[Splitlink]

It's all Greek to me, but I should say that the chances of the 55th trade going up, or down, were 50-50.

 

[hhiusa]

This statistical question you have raised hhiusa is pure mathematical and so its real meaning in the real world is of limited use.

My question back to you would therefore be .............Why ?

You mention that 100% of the sample - ie 54 trades - were profitable.

OK - so then go on to show that the Z score is 2.1 and positive

So the probability is very high

Ok in the real world the 55th trade could still fail - and that is the most important part of what you need to know

Whether you are 95% confident that 91.8% of all future trades will be profitable or not is of NO significance in the real world to you saying you are only 86% confident of 94.2% of all future trades will be profitable.

Personally - I reckon you need a larger sample - ie >100+ or even better >1000

Otherwise stick 3 Maths Professors in a room together - and I bet one would disagree with the other 2 and would be able to explain with another formula that the assumption you have made are incorrect

Last point

What ever you do - dont ask any American Maths Professors - stick with reliable European ones - Harvard and MIT students are not the World's best - as I am sure you want to prove next ;-))

Did you really feel the need to post if you weren't going to answer or couldn't not answer the math question. I don't really care about your views on mathematical finance and its use in the real world. Do you have anything worthwhile to say about the math.

The Chi-squared distribution takes the sample size into account. The only need for a higher sample size is the need to increase your confidence. If you were following the math you would understand that.

 

[NVP]

we are not worthy then HH......you know your math dude

but do you know how to kick butt trading ?.........that's what the T2win forum is all about ......

N

 

[ffsear]

. Do you have anything worthwhile to say about the math..

Its not yours!

http://math.stackexchange.com/quest...on-finite-population-with-unknown-cardinality

 

[Forexmospherian]

Did you really feel the need to post if you weren't going to answer or couldn't not answer the math question. I don't really care about your views on mathematical finance and its use in the real world. Do you have anything worthwhile to say about the math.

The Chi-squared distribution takes the sample size into account. The only need for a higher sample size is the need to increase your confidence. If you were following the math you would understand that.

To answer the important part underlined -

Do you have anything worthwhile to say about the math ?

Yes

grammatical error - no "s" on math

Also learn from this - Trading is not a pure mathematical science

Repeat - Trading is not a pure mathematical science.

You can mention chi squared distribution - non central beta distribution - pareto's distribution - non central t distribution etc etc - in fact all the theories you can come u with - BUT - its of no real use in the real trading environment


So - stick that in your pipe - and smoke it

Regards


F

 

[hhiusa]

Its not yours!

http://math.stackexchange.com/quest...on-finite-population-with-unknown-cardinality

What an idiot you are! It's my account. I thought I would ask the same question here since it went unanswered.

 

[hhiusa]

To answer the important part underlined -

Do you have anything worthwhile to say about the math ?

Yes

grammatical error - no "s" on math

Also learn from this - Trading is not a pure mathematical science

Repeat - Trading is not a pure mathematical science.

You can mention chi squared distribution - non central beta distribution - pareto's distribution - non central t distribution etc etc - in fact all the theories you can come u with - BUT - its of no real use in the real trading environment


So - stick that in your pipe - and smoke it

Regards


F

Whatever dude! It works great for me as those 54 trades are real for 1 equity over 7 years. Look up the Black Scholes asset pricing model which uses stochastic partial differential equations. You use stochastic optimization to optimize the equations. Some EMAs are partial differential equations which use a smoothing variable μ. Ds = μΔS_t + σS_tW_t. σ is volatility and W_t is a Wiener process. Math definitely has a place in finance. Investment firms spend billions on mathetical research and hire matheticians with little or no finance experience over those who are basically glorified salesmen (stock brokers). Obviously you have absolutely no research and nominal mathematical prowess.

 

[hhiusa]

we are not worthy then HH......you know your math dude

but do you know how to kick butt trading ?.........that's what the T2win forum is all about ......

N

Thank you NVP! I have more good days than bad.

 

[Forexmospherian]

Whatever dude! It works great for me as those 54 trades are real for 1 equity over 7 years. Look up the Black Scholes asset pricing model which uses stochastic partial differential equations. You use stochastic optimization to optimize the equations. Some EMAs are partial differential equations which use a smoothing variable μ. Ds = μΔS_t + σS_tW_t. σ is volatility and W_t is a Wiener process. Math definitely has a place in finance. Investment firms spend billions on mathetical research and hire matheticians with little or no finance experience over those who are basically glorified salesmen (stock brokers). Obviously you have absolutely no research and nominal mathematical prowess.

Investment firms spend billions on mathematical ( spelling mistake again - that rules you out of being a previous multi nic ) research and hire mathematicians ( another spelling mistake - proving beyond doubt your attention to detail - no good for any wannabee maths Pro )


Yes you are so correct

Do you mean these investment and finance companies -

https://en.wikipedia.org/wiki/List_...es_during_the_2007–12_global_financial_crisis

Keep providing me with jokes - I can hold the mirror up for you

Regards

F

 

[hhiusa]

Investment firms spend billions on mathematical ( spelling mistake again - that rules you out of being a previous multi nic ) research and hire mathematicians ( another spelling mistake - proving beyond doubt your attention to detail - no good for any wannabee maths Pro )


Yes you are so correct

Do you mean these investment and finance companies -

https://en.wikipedia.org/wiki/List_...es_during_the_2007–12_global_financial_crisis

Keep providing me with jokes - I can hold the mirror up for you

Regards

F

Your anger seriously amuses me. If the only argument you can find is that I made some typos, then I'll be just fine. Since math isn't your strength, I honestly don't know what you use to trade. I don't use math by itself and I never stated that I did. I magine you could watch the news and fly by the seat of your pants.

 

[Forexmospherian]

Your anger seriously amuses me. If the only argument you can find is that I made some typos, then I'll be just fine. Since math isn't your strength, I honestly don't know you use to trade. I don't use math by itself and I never stated that I did. I magine you could watch the news and fly by the seat of your pants.

Apologies

You have confirmed you are not who I thought you were ?

I had been thinking you were another wind up merchant using another nic - and I am wrong

You did it again in your last comment - ie said math instead of maths - proving you are probably from the US and you also confirmed in another comment to ffsears that you are studying biochemistry in California.

Good Trading to you and I am pleased you don't just use maths formulations and theory in isolation

Regards

F

 

[hhiusa]

Apologies

You have confirmed you are not who I thought you were ?

I had been thinking you were another wind up merchant using another nic - and I am wrong

You did it again in your last comment - ie said math instead of maths - proving you are probably from the US and you also confirmed in another comment to ffsears that you are studying biochemistry in California.

Good Trading to you and I am pleased you don't just use maths formulations and theory in isolation

Regards

F

I invest in order to pay for the upcoming medical school bills. Studying biochemistry is one of the only ways to afford myself the lifestyle I had growing up. Besides, I was terrible in history and creative writing. The humanities are to me like the sciences are to most people. My father said "you can pay me now or you can pay me later" metaphorically speaking. He was referring to the fact that I could study a "b.s. degree" like something in the humanities or I could study "something important". By "b.s. degree" he was certainly not referring to bachelor's of science if you catch my drift.

What did you study in university? I hear from my British American friends that university is insanely cheaper there. Medical school is about $250,000 here. Even low end colleges here cost more than a car. It reminds me of a song by the Sohodolls. "Save up all your USDs, for British universities".

 

[Forexmospherian]

I invest in order to pay for the upcoming medical school bills. Studying biochemistry is one of the only ways to afford myself the lifestyle I had growing up. Besides, I was terrible in history and creative writing. The humanities are to me like the sciences are to most people. My father said "you can pay me now or you can pay me later" metaphorically speaking. He was referring to the fact that I could study a "b.s. degree" like something in the humanities or I could study "something important". By "b.s. degree" he was certainly not referring to bachelor's of science if you catch my drift.

What did you study in university? I hear from my British American friends that university is insanely cheaper there. Medical school is about $250,000 here. Even low end colleges here cost more than a car. It reminds me of a song by the Sohodolls. "Save up all your USDs, for British universities".

I went to University in Birmingham UK approx 40 years ago.

I managed to achieve 5 A levels and HND in Business studies before obtaining a 2 2 Honours Degree in Economics ( only average ) and then started my own business within one year of leaving.

Nowadays - my daughter who is at Nottingham University pays equivalent to approx $6500 per annum for her fees - for a 3 year BA course in Marketing and Business studies. Total cost over 3 years with accommodation and living expenses etc would be in total under $60k - so yes a lot cheaper than over in the States.

I don't know the cost for International students - but I am sure a lot less than you are paying

I have also heard Americans having major surgery etc having to pay $100k as well if they have not got medical insurance. Here in the UK - the National Health Service is Free - yes you can go private - and so there is a choice.

Saying that I love California and its lifestyle - so you do have other advantages - you have just got to make sure you earn the big bucks and stay healthy ;-)


Regards

F

 

[hhiusa]

I went to University in Birmingham UK approx 40 years ago.

I managed to achieve 5 A levels and HND in Business studies before obtaining a 2 2 Honours Degree in Economics ( only average ) and then started my own business within one year of leaving.

Nowadays - my daughter who is at Nottingham University pays equivalent to approx $6500 per annum for her fees - for a 3 year BA course in Marketing and Business studies. Total cost over 3 years with accommodation and living expenses etc would be in total under $60k - so yes a lot cheaper than over in the States.

I don't know the cost for International students - but I am sure a lot less than you are paying

I have also heard Americans having major surgery etc having to pay $100k as well if they have not got medical insurance. Here in the UK - the National Health Service is Free - yes you can go private - and so there is a choice.

Saying that I love California and its lifestyle - so you do have other advantages - you have just got to make sure you earn the big bucks and stay healthy ;-)


Regards

F

I don't know why but I have never really thought about the health care system. I only know of the costs because some my relatives are in the medical field. I go to the doctor when I am sick or about every 3 months. I never get a huge bill. Even if I was living in England, I would choose to go private. Doctors are paid more here than they are anywhere. That inexpensive health care comes at a cost to the doctors.

Netherlands - $253,000
Australia - $247,000
United States - $230,000
Belgium - $188,000
Canada - $161,000
United Kingdom - $150,000
Ireland - $149,000
Switzerland - $130,000
Denmark - $91,000

In 16th place is Greece - $67,000

An overview of the salaries for different specialities
Radiology: $315,000
Orthopedics: $315,000
Cardiology: $314,000
Plastic surgery: $270,000
General surgery: $265,000
Obstetrics/Gynecology: $220,000
Psychiatry: $170,000
Pediatrics: $156,000

http://www.insidermonkey.com/blog/16-highest-paying-countries-for-doctors-314590/

 

[VielGeld]

Been a long while since I've studied statistics, but I'd wager the formula in the OP is for the 55th trade and not the subsequent ones. For each subsequent trade, you should see a slightly lower % until lim > 0.

 

[hhiusa]

Been a long while since I've studied statistics, but I'd wager the formula in the OP is for the 55th trade and not the subsequent ones. For each subsequent trade, you should see a slightly lower % until lim > 0.

That is only part of the picture. That describes a transition state matrix. The probability of predicting k steps into the futures; however, I am only predicting 1 step at a time. Upon the 55th trade, it will become the present and the Chi-squared distribution will be recalculated for n-1 degrees of freedom. As n-1 reaches infinity, the window will squeeze into a single value. It doesn't increase the accuracy of the system but it increases the accuracy of the predictions about its accuracy. A new sample mean and standard deviation will be calculated and normalized. This will produce a new probability window. I have it set to monitor the permutations of 50 PDEs. This works similar to stochastic gradient descent. After each step, it determines the next optimal step.

I was also interested in having the math checked.