difference between pdf and accumulative frequency ?

model · 2012-02-01 19:35:59

Are probability density function and accumulative frequency same thing ?

bobbym · 2012-02-01 20:12:03

Hi model;

For one thing a Cumulative frequency is used mostly for discrete data.

http://www.mathsisfun.com/definitions/c … uency.html

PDF is for continuous data. A Cumulative Distribution Function or CDF is closer to it.

model · 2012-02-01 22:42:34

Hy one second,

I read out binomial random variables can be solved from combination nC(r) for finding the probability and i successfully represented probabilities in form of histogram .

On the other hand, I maked histogram of some pixels using this way .

Data : i have pixel values ./
frequency : the repetition of pixel values
Accumulative frequency : add current and previous frequency .
probability : divide each accumulative frequency by total number of data or class interval width .

Now My question is combination and the other way that i explained . both are same logically .
Right ?

bobbym · 2012-02-01 22:46:22

Hi model;

I do not know. Do you have a small example of what you mean?

model · 2012-02-01 22:55:38

hmm yes ..

Example of binomial random variable :
How many ways are there to chose 2 times out of 3.
nCr(2,3) = 3! /2! (3-2)!

The above way is called combination .

Now suppose we have some values or pixels values like

pixels frequency accumulative frequency
1 1 is repeated 2 times 2
1 2 is repeated 2 times 4
2 3 is repeated 1 time 5
3
2

and total probability is
2/5+ 4/5 + 5 /5 = 2.2

bobbym · 2012-02-01 22:59:48

Hi;

to chose 2 times out of 3.
nCr(2,3) = 3! /2! (3-2)!

Hold it for a second. Not nitpicking here but we have to speak the same language if we are going to communicate.

Ncr(3,2) means 3 choose 2. From 3 objects choose 2 of them. Ncr(2,3) means 2 choose 3 which can not be done and equals 0.

model · 2012-02-01 23:02:56

bobbym wrote:

Hi;
to chose 2 times out of 3.
nCr(2,3) = 3! /2! (3-2)!
Hold it for a second. Not nitpicking here but we have to speak the same language if we are going to communicate.
Ncr(3,2) means 3 choose 2. From 3 objects choose 2 of them. Ncr(2,3) means 2 choose 3 which can not be done and equals 0.

ohh sorry i wrote is wrong.
but anyways , logically the probability from combination and the way that i did for histogram of some pixels .

Logically both have same meaning . Right ?

Last edited by model (2012-02-01 23:05:26)

bobbym · 2012-02-01 23:09:08

Hi model;

and total probability is
2/5+ 4/5 + 5 /5 = 2.2

Let me help you out here. A probability can never be greater than 1. So what are we computing here?

model · 2012-02-01 23:10:40

if yes then I have another formula for Binomial probability

Pr(X= r) = nCr(p^r)q^(n-r) where n and p are binomial parameters and q = i-p .

What is the purpose of this ?
What is the actual meaning of that ?
Is combination not just enough for finding probability ?

model · 2012-02-01 23:12:59

bobbym wrote:

Hi model;
and total probability is
2/5+ 4/5 + 5 /5 = 2.2
Let me help you out here. A probability can never be greater than 1. So what are we computing here?

ohh yes . the same question i have .
I do't know but i read out the formula of combination for finding probability from book.

bobbym · 2012-02-01 23:16:16

Hi;

A probability is always a ratio. It can be defined as

which means successes over successes + failures. In other words it is a fraction.

A binomial like Ncr(3,2) is a whole number. It is always a whole number. It counts something. So it is never enough to be a probability except when it equals 1 or 0.

model · 2012-02-01 23:19:39

bobbym wrote:

Hi;
A probability is always a ratio. It can be defined as
which means successes over successes + failures. In other words it is a fraction.
A binomial like Ncr(3,2) is a whole number. It is always a whole number. It counts something. So it is never enough to be a probability except when it equals 1.

Hy,

but our probability is > 1 that's 2.2 . Although its in fraction but its > 1 .

model · 2012-02-01 23:23:29

bobbym wrote:

Hi;
A probability is always a ratio. It can be defined as
which means successes over successes + failures. In other words it is a fraction.
A binomial like Ncr(3,2) is a whole number. It is always a whole number. It counts something. So it is never enough to be a probability except when it equals 1 or 0.

bobbym · 2012-02-01 23:24:47

That is what I am saying, a probability is never greater than 1.

P(of something happening) = 0 this means it can never happen. Example: I roll a dice and it comes up 7. Can not happen P = 0

P(of something happening) = 1 this means it always happens. Example: I flip a coin and it comes either heads or tails. Happens all the time P = 1.

All other probabilities are between 0 and 1.

model · 2012-02-01 23:29:15

bobbym wrote:

That what I am saying, a probability is never greater than 1.
P(of something happening) = 0 this means it can never happen. Example: I roll a dice and it comes up 7. Can not happen P = 0

P(of something happening) = 1 this means it always happens. Example: I flip a coin and it comes either heads or tails. Happens all the time P = 1.
All other probabilities are between 0 and 1.

Well from the above discussion,
I think, Probability which is a fraction between 0 and 1 .
Probability will happen only if data set have whole numbers except 0 or 1 .
if data set have 1 then probability will be 0 .

like in the above case , i got 2.2 . here probability is 0.

but if i have data set like 2 , 3 ,2 ,5 , 5 then i get probability = 1 .

bobbym · 2012-02-01 23:35:29

Hi model;

but if i have data set like 2 , 3 ,2 ,5 , 5 then i get probability = 1

You have 5 pieces of data. The probability of getting a 2 is 2 / 5. The probability of getting a 5 is 2 / 5. The probability of getting a 3 is 1 / 5.

P( of getting a 2, 3 or 5 ) =1 / 5 + 2 / 5 + 2 / 5 = 1

model · 2012-02-01 23:56:38

Hy ,

I have another formula for binomial profitability that's

Pr(X= r) = nCr(p^r)q^(n-r) where n and p are binomial parameters and q = i-p .

This give real and right probability between 0 and 1 .

then what is the use of simple combination nCr() = n! /r!(n-r)!

bobbym · 2012-02-02 00:03:21

then what is the use of simple combination nCr() = n! /r!(n-r)!

This counts the number of ways to choose or select something from a collection of objects. It is not a probability.

For instance we have 3 books, a math book, an english book and a history book.

M E H

In how many ways can I choose or select 2 books from that group of 3.

Ncr(3,2) = 3

If you count them manually
(M E)
(M H)
(E H)
that is 3 just like the Ncr said.

Do not confuse the binomial distribution which is a probability with a binomial which is a count of things.

model · 2012-02-04 15:49:39

bobbym wrote:

then what is the use of simple combination nCr() = n! /r!(n-r)!
This counts the number of ways to choose or select something from a collection of objects. It is not a probability.
For instance we have 3 books, a math book, an english book and a history book.
M E H
In how many ways can I choose or select 2 books from that group of 3.
Ncr(3,2) = 3
If you count them manually
(M E)
(M H)
(E H)
that is 3 just like the Ncr said.
Do not confuse the binomial distribution which is a probability with a binomial which is a count of things.

Oh i see . Thanks Sir : )

bobbym · 2012-02-04 16:41:56

Hi model;

Your welcome glad to help.

model · 2012-02-06 00:23:16

HY ,How can Binomial theorem or distribution help on binary image ?

let say i have an image like

1 0 1 1 1 1
0 0 1 1 1 1
0 0 1 1 1 1
0 0 0 0 0 0
0 0 0 0 0 0
1 1 0 0 0 0
1 1 1 1 1 1

How can binomial distribution help me on the above binary matrix ?

bobbym · 2012-02-06 00:25:03

Hi model;

How can binomial distribution help me on the above binary matrix ?

It can't, not until you tell me what you want to do with that matrix.

model · 2012-02-06 00:29:24

hmm well actually my friends told me to track moving object using kalman filter and kalman filter relate to Bayes's theorem that mean Bayes's theorem may be also help to talk moving objects .

So, actually i have to track moving objects. Can Bayes's theorem or distribution can help me with that ?

Please help me to understand it for tracking motion objects

Last edited by model (2012-02-06 00:31:26)

bobbym · 2012-02-06 00:43:25

Hi model;

A Kalman filter is for tracking moving objects and is used in missile guidance sytems and GPS. It is a Markov chain and a whole lot more. Can you get more info out or your friend?

model · 2012-02-06 00:45:41

bobbym wrote:

Hi model;
A Kalman filter is for tracking moving objects and is used in missile guidance sytems and GPS. It is a Markov chain and a whole lot more. Can you get more info out or your friend?

Well but let's play with Bayes' distribution on matrix.
Then latter i would like to move to Kalman filter . because i have to learn about Kalman but before that i wanna know that can Bayes' could help in tracking ?

Last edited by model (2012-02-06 00:47:14)

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#1 2012-02-01 19:35:59

difference between pdf and accumulative frequency ?

#2 2012-02-01 20:12:03

Re: difference between pdf and accumulative frequency ?

#3 2012-02-01 22:42:34

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