User talk:Lothar.brendel - Revision history

Lothar.brendel: /* Florian's eCDF */ interval

2024-07-10T16:34:39Z

Florian's eCDF: interval

← Older revision		Revision as of 18:34, 10 July 2024
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	:: \(p_{n_i} = \frac{c(n_i) - c(n_{i-1})}{n_i - n_{i-1}}\) is the assignment. There is actually no particular reason I chose this. In the picture of continuous random variables, any discretized derivative should, ignoring the discretization error, work just fine and should converge to the actual PDF for an infinitely large sample. If this is true for discrete random variables as well (i.e. that it converges to the correct probabilities), I do not know. --[[User:Florian\|Florian]] ([[User talk:Florian\|talk]]) 16:47, 10 July 2024 (CEST)		:: \(p_{n_i} = \frac{c(n_i) - c(n_{i-1})}{n_i - n_{i-1}}\) is the assignment. There is actually no particular reason I chose this. In the picture of continuous random variables, any discretized derivative should, ignoring the discretization error, work just fine and should converge to the actual PDF for an infinitely large sample. If this is true for discrete random variables as well (i.e. that it converges to the correct probabilities), I do not know. --[[User:Florian\|Florian]] ([[User talk:Florian\|talk]]) 16:47, 10 July 2024 (CEST)

	::: How ~~does~~ the normalization operation for this look like? --[[User:Lothar.brendel\|Lothar]] ([[User talk:Lothar.brendel\|talk]]) 17:20, 10 July 2024 (CEST)		::: How would the normalization operation for this look like? IMHO, that constant value should be assigned to the ''interval'' \((n_{i-1},n_i]\). --[[User:Lothar.brendel\|Lothar]] ([[User talk:Lothar.brendel\|talk]]) 18:34, 10 July 2024 (CEST)

Lothar.brendel: /* Florian's eCDF */ normalize?

2024-07-10T15:21:16Z

Florian's eCDF: normalize?

← Older revision		Revision as of 17:21, 10 July 2024
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	: When dropping \(n\in\mathbb N\), to ''which'' values \(n\) do you assign ficticious probabability(-density)-values and why? --[[User:Lothar.brendel\|Lothar]] ([[User talk:Lothar.brendel\|talk]]) 15:51, 10 July 2024 (CEST)		: When dropping \(n\in\mathbb N\), to ''which'' values \(n\) do you assign ficticious probabability(-density)-values and why? --[[User:Lothar.brendel\|Lothar]] ([[User talk:Lothar.brendel\|talk]]) 15:51, 10 July 2024 (CEST)

	\(p_{n_i} = \frac{c(n_i) - c(n_{i-1})}{n_i - n_{i-1}}\) is the assignment. There is actually no particular reason I chose this. In the picture of continuous random variables, any discretized derivative should, ignoring the discretization error, work just fine and should converge to the actual PDF for an infinitely large sample. If this is true for discrete random variables as well (i.e. that it converges to the correct probabilities), I do not know.		:: \(p_{n_i} = \frac{c(n_i) - c(n_{i-1})}{n_i - n_{i-1}}\) is the assignment. There is actually no particular reason I chose this. In the picture of continuous random variables, any discretized derivative should, ignoring the discretization error, work just fine and should converge to the actual PDF for an infinitely large sample. If this is true for discrete random variables as well (i.e. that it converges to the correct probabilities), I do not know. --[[User:Florian\|Florian]] ([[User talk:Florian\|talk]]) 16:47, 10 July 2024 (CEST)

	--[[User:~~Florian~~\|~~Florian~~]] ([[User talk:~~Florian~~\|talk]]) 16:47, 10 July 2024 (CEST)		::: How does the normalization operation for this look like? --[[User:Lothar.brendel\|Lothar]] ([[User talk:Lothar.brendel\|talk]]) 17:20, 10 July 2024 (CEST)

Florian: /* Florian's eCDF */

2024-07-10T14:47:36Z

Florian's eCDF

← Older revision		Revision as of 16:47, 10 July 2024
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	: When dropping \(n\in\mathbb N\), to ''which'' values \(n\) do you assign ficticious probabability(-density)-values and why? --[[User:Lothar.brendel\|Lothar]] ([[User talk:Lothar.brendel\|talk]]) 15:51, 10 July 2024 (CEST)		: When dropping \(n\in\mathbb N\), to ''which'' values \(n\) do you assign ficticious probabability(-density)-values and why? --[[User:Lothar.brendel\|Lothar]] ([[User talk:Lothar.brendel\|talk]]) 15:51, 10 July 2024 (CEST)

			\(p_{n_i} = \frac{c(n_i) - c(n_{i-1})}{n_i - n_{i-1}}\) is the assignment. There is actually no particular reason I chose this. In the picture of continuous random variables, any discretized derivative should, ignoring the discretization error, work just fine and should converge to the actual PDF for an infinitely large sample. If this is true for discrete random variables as well (i.e. that it converges to the correct probabilities), I do not know.

			--[[User:Florian\|Florian]] ([[User talk:Florian\|talk]]) 16:47, 10 July 2024 (CEST)

Lothar.brendel: n aus R

2024-07-10T13:52:03Z

n aus R

← Older revision		Revision as of 15:52, 10 July 2024
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			== Florian's eCDF ==

	Good to know that "empirical probability" is a synonym for the relative frequency.		Good to know that "empirical probability" is a synonym for the relative frequency.

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	--[[User:Florian\|Florian]] ([[User talk:Florian\|talk]]) 15:03, 10 July 2024 (CEST)		--[[User:Florian\|Florian]] ([[User talk:Florian\|talk]]) 15:03, 10 July 2024 (CEST)

			: When dropping \(n\in\mathbb N\), to ''which'' values \(n\) do you assign ficticious probabability(-density)-values and why? --[[User:Lothar.brendel\|Lothar]] ([[User talk:Lothar.brendel\|talk]]) 15:51, 10 July 2024 (CEST)

Florian at 13:03, 10 July 2024

2024-07-10T13:03:43Z

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	--[[User:Florian\|Florian]] ([[User talk:Florian\|talk]]) 14:54, 10 July 2024 (CEST)		--[[User:Florian\|Florian]] ([[User talk:Florian\|talk]]) 14:54, 10 July 2024 (CEST)

			By this logic, I am quite confused, because the PDF estimates are normalized to one. I would have expected that I need an integral for the normalization if I assumed continuous random numbers in the beginning.

			--[[User:Florian\|Florian]] ([[User talk:Florian\|talk]]) 15:03, 10 July 2024 (CEST)

Florian at 12:54, 10 July 2024

2024-07-10T12:54:44Z

← Older revision	Revision as of 14:54, 10 July 2024
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		Good to know that "empirical probability" is a synonym for the relative frequency.

		My own idea behind all this seemed way simpler to me at the time; although, I am not sure how to properly show that it does what it should at the moment. Basically, I conveniently forgot that the agglomerate sizes are restricted to natural numbers. From there, I can estimate the probability density by estimating the derivative of the CDF, in my case as discretized derivatives using the eCDF. However, this means that the values I calculated are estimates of the PDF, not of the probabilities as I originally wanted.

		--[[User:Florian\|Florian]] ([[User talk:Florian\|talk]]) 14:54, 10 July 2024 (CEST)

Lothar.brendel: wipe

2024-07-10T12:37:28Z

wipe

← Older revision		Revision as of 14:37, 10 July 2024
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	~~<small>(Mail-Tests erfolgreich)</small>~~

Lothar.brendel: wipe

2024-05-07T08:17:02Z

wipe

← Older revision		Revision as of 10:17, 7 May 2024
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	~~Nein, ich bekomme keinerlei Benachrichtigung, du? --Frederike~~		<small>(Mail-Tests erfolgreich)</small>

	~~Nicht als~~ Mail~~, nein, bloß in der Watchlist. :-( -- Lothar~~

	~~Test: lorem ipsum dolor -~~- ~~zick~~

	~~Ein hoffentlich letzter Test...~~

Frederike at 12:14, 15 February 2024

2024-02-15T12:14:31Z

← Older revision		Revision as of 14:14, 15 February 2024
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	Test: lorem ipsum dolor -- zick		Test: lorem ipsum dolor -- zick

			Ein hoffentlich letzter Test...

Lothar.brendel: Reverted edits by Test (talk) to last revision by Admin ude

2024-02-08T12:37:32Z

Reverted edits by Test (talk) to last revision by Admin ude

← Older revision		Revision as of 14:37, 8 February 2024
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	Test: lorem ipsum dolor -- zick		Test: lorem ipsum dolor -- zick

	~~Ein weiterer Mail-Test. -- Test-User~~