Abuse of notation: Difference between revisions

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In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair Template:Dice. The possible values are 1, 2, 3, 4, 5, 6, and each time the Template:Dice is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n). With these conventions, the cumulative distribution function (CDF) of the discrete uniform distribution can be expressed, for any k ∈ [a,b], as

F (k; a, b) = \frac{⌊ k ⌋ - a + 1}{b - a + 1}

Estimation of maximum

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. This example is described by saying that a sample of k observations is obtained from a uniform distribution on the integers $1, 2, \dots, N$ , with the problem being to estimate the unknown maximum N. This problem is commonly known as the German tank problem, following the application of maximum estimation to estimates of German tank production during World War II.

The UMVU estimator for the maximum is given by

\hat{N} = \frac{k + 1}{k} m - 1 = m + \frac{m}{k} - 1

where m is the sample maximum and k is the sample size, sampling without replacement.^[1]^[2] This can be seen as a very simple case of maximum spacing estimation.

The formula may be understood intuitively as:

"The sample maximum plus the average gap between observations in the sample",

the gap being added to compensate for the negative bias of the sample maximum as an estimator for the population maximum.^{[notes 1]}

This has a variance of^[1]

\frac{1}{k} \frac{(N - k) (N + 1)}{(k + 2)} \approx \frac{N^{2}}{k^{2}} for small samples k ≪ N

so a standard deviation of approximately $N / k$ , the (population) average size of a gap between samples; compare $\frac{m}{k}$ above.

The sample maximum is the maximum likelihood estimator for the population maximum, but, as discussed above, it is biased.

If samples are not numbered but are recognizable or markable, one can instead estimate population size via the capture-recapture method.

Random permutation

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. See rencontres numbers for an account of the probability distribution of the number of fixed points of a uniformly distributed random permutation.

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

55 yrs old Metal Polisher Records from Gypsumville, has interests which include owning an antique car, summoners war hack and spelunkering. Gets immense motivation from life by going to places such as Villa Adriana (Tivoli).

my web site - summoners war hack no survey ios Template:Common univariate probability distributions

su:Sebaran seragam#Kasus diskrit

↑ ^1.0 ^1.1 Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

Cite error: <ref> tags exist for a group named "notes", but no corresponding <references group="notes"/> tag was found

[Johnson-1] 1.0 ^1.1 Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

[Johnson2-2] Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

[1]

[2]

[notes 1]

@@ Line 1: / Line 1: @@
-Im Eduardo and was born on 12 March 1978. My hobbies are Element collecting and Vehicle restoration.<br><br>Here is my homepage ... Fifa 15 Coin Generator ([http://Www.sanyangyasuoji.com/plus/guestbook.php Www.Sanyangyasuoji.com])
+<!--- EDITORS! Please see [[Wikipedia:WikiProject Probability#Standards]] for a discussion of standards used for probability distribution articles such as this one --->
+{{Probability distribution|
+  name       =discrete uniform|
+  type       =mass|
+  pdf_image  =[[Image:Uniform discrete pmf svg.svg|325px|Discrete uniform probability mass function for ''n'' = 5]]<br /><small>''n'' = 5 where ''n'' = ''b''&nbsp;&minus;&nbsp;''a''&nbsp;+&nbsp;1</small>|
+  cdf_image  =[[Image:Dis Uniform distribution CDF.svg|325px|Discrete uniform cumulative distribution function for ''n'' = 5]]<br /><small></small>|
+  parameters =<math>a \in (\dots,-2,-1,0,1,2,\dots)\,</math><br /><math>b \in (\dots,-2,-1,0,1,2,\dots), b \ge a</math><br /><math>n=b-a+1\,</math>|
+  support    =<math>k \in \{a,a+1,\dots,b-1,b\}\,</math>|
+  pdf        =<math>\frac{1}{n}</math>|
+  cdf        =<math> \frac{\lfloor k \rfloor -a+1}{n} </math>|
+  mean       =<math>\frac{a+b}{2}\,</math>|
+  median     =<math>\frac{a+b}{2}\,</math>|
+  mode       =N/A|
+  variance   =<math>\frac{n^2-1}{12}</math>|
+  skewness   =<math>0\,</math>|
+  kurtosis   =<math>-\frac{6(n^2+1)}{5(n^2-1)}\,</math>|
+  entropy    =<math>\ln(n)\,</math>|
+  mgf        =<math>\frac{e^{at}-e^{(b+1)t}}{n(1-e^t)}\,</math>|
+  char       =<math>\frac{e^{iat}-e^{i(b+1)t}}{n(1-e^{it})}</math>|
+}}
+In [[probability theory]] and [[statistics]], the '''discrete uniform distribution''' is a [[Symmetric distribution|symmetric]] [[discrete probability distribution|probability distribution]] whereby a finite number of values are equally likely to be observed; every one of ''n'' values has equal probability ''1/n''. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".
+A simple example of the discrete uniform distribution is throwing a fair {{dice}}. The possible values are 1, 2, 3, 4, 5, 6, and each time the {{dice}} is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.
+The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval ''[a,b]'', so that ''a,b'' become the main parameters of the distribution (often one simply considers the interval ''[1,n]'' with the single parameter ''n''). With these conventions, the [[cumulative distribution function]] (CDF) of the discrete uniform distribution can be expressed, for any ''k'' ∈ ''[a,b]'', as
+:<math>F(k;a,b)=\frac{\lfloor k \rfloor -a + 1}{b-a+1}</math>
+==Estimation of maximum==
+{{main|German tank problem}}
+This example is described by saying that a sample of ''k'' observations is obtained from a uniform distribution on the integers <math>1,2,\dots,N</math>, with the problem being to estimate the unknown maximum ''N''.  This problem is commonly known as the [[German tank problem]], following the application of maximum estimation to estimates of German tank production during [[World War II]].
+The [[UMVU]] estimator for the maximum is given by
+:<math>\hat{N}=\frac{k+1}{k} m - 1 = m + \frac{m}{k} - 1</math>
+where ''m'' is the [[sample maximum]] and ''k'' is the [[sample size]], sampling without replacement.<ref name="Johnson">{{citation
+|last=Johnson
+|first=Roger
+|title=Estimating the Size of a Population
+|year=1994
+|journal=[http://www.rsscse.org.uk/ts/index.htm Teaching Statistics]
+|volume=16
+|issue=2 (Summer)
+|doi=10.1111/j.1467-9639.1994.tb00688.x
+}}</ref><ref name="Johnson2">{{citation
+|last=Johnson
+|first=Roger
+|contribution=Estimating the Size of a Population
+|title=Getting the Best from Teaching Statistics
+|year=2006
+|url=http://www.rsscse.org.uk/ts/gtb/contents.html
+|contribution-url=http://www.rsscse.org.uk/ts/gtb/johnson.pdf
+}}</ref> This can be seen as a very simple case of [[maximum spacing estimation]].
+The formula may be understood intuitively as:
+:"The sample maximum plus the average gap between observations in the sample",
+the gap being added to compensate for the negative bias of the sample maximum as an estimator for the population maximum.<ref group="notes">The sample maximum is never more than the population maximum, but can be less, hence it is a [[biased estimator]]: it will tend to ''underestimate'' the population maximum.</ref>
+This has a variance of<ref name="Johnson"/>
+:<math>\frac{1}{k}\frac{(N-k)(N+1)}{(k+2)} \approx \frac{N^2}{k^2} \text{ for small samples } k \ll N</math>
+so a standard deviation of approximately <math>N/k</math>, the (population) average size of a gap between samples; compare <math>\frac{m}{k}</math> above.
+The sample maximum is the [[maximum likelihood]] estimator for the population maximum, but, as discussed above, it is biased.
+If samples are not numbered but are recognizable or markable, one can instead estimate population size via the [[capture-recapture]] method.
+==Random permutation==
+{{main|Random permutation}}
+See [[rencontres numbers]] for an account of the probability distribution of the number of fixed points of a uniformly distributed [[random permutation]].
+==See also==
+* [[Delta distribution]]
+* [[Uniform distribution (continuous)]]
+==Notes==
+{{reflist|group=notes}}
+==References==
+{{reflist}}
+{{ProbDistributions|discrete-finite}}
+{{Common univariate probability distributions}}
+{{DEFAULTSORT:Uniform Distribution (Discrete)}}
+[[Category:Discrete distributions]]
+[[Category:Probability distributions]]
+[[su:Sebaran seragam#Kasus diskrit]]

Abuse of notation: Difference between revisions

Revision as of 23:32, 25 December 2013

Contents

Estimation of maximum

Random permutation

See also

Notes

References

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Abuse of notation: Difference between revisions

Revision as of 23:32, 25 December 2013

Estimation of maximum

Random permutation

See also

Notes

References

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