Energy operator: Difference between revisions

Revision as of 17:28, 5 December 2013

In probability theory, the arcsine distribution is the probability distribution whose cumulative distribution function is

F (x) = \frac{2}{π} \arcsin (\sqrt{x}) = \frac{\arcsin (2 x - 1)}{π} + \frac{1}{2}

for 0 ≤ x ≤ 1, and whose probability density function is

f (x) = \frac{1}{π \sqrt{x (1 - x)}}

on (0, 1). The standard arcsine distribution is a special case of the beta distribution with α = β = 1/2. That is, if $X$ is the standard arcsine distribution then $X \sim B e t a (\frac{1}{2}, \frac{1}{2})$

The arcsine distribution appears

in the Lévy arcsine law;
in the Erdős arcsine law;
as the Jeffreys prior for the probability of success of a Bernoulli trial.

Generalization

Template:Probability distribution

Arbitrary bounded support

The distribution can be expanded to include any bounded support from a ≤ x ≤ b by a simple transformation

F (x) = \frac{2}{π} \arcsin (\sqrt{\frac{x - a}{b - a}})

for a ≤ x ≤ b, and whose probability density function is

f (x) = \frac{1}{π \sqrt{(x - a) (b - x)}}

on (a, b).

Shape factor

The generalized standard arcsine distribution on (0,1) with probability density function

\begin{aligned} f (x; α) & = \frac{\sin π α}{π} x^{- α} (1 - x)^{α - 1} \end{aligned}

is also a special case of the beta distribution with parameters $B e t a (1 - α, α)$ .

Note that when $α = \frac{1}{2}$ the general arcsine distribution reduces to the standard distribution listed above.

Properties

Arcsine distribution is closed under translation and scaling by a positive factor
- If $X \sim A r c s i n e (a, b) then k X + c \sim A r c s i n e (a k + c, b k + c)$
The square of an arc sine distribution over (-1, 1) has arc sine distribution over (0, 1)
- If $X \sim A r c s i n e (- 1, 1) then X^{2} \sim A r c s i n e (0, 1)$

Related distributions

If U and V are i.i.d uniform (−π,π) random variables, then $\sin (U)$ , $\sin (2 U)$ , $- \cos (2 U)$ , $\sin (U + V)$ and $\sin (U - V)$ all have a standard arcsine distribution
If $X$ is the generalized arcsine distribution with shape parameter $α$ supported on the finite interval [a,b] then $\frac{X - a}{b - a} \sim B e t a (1 - α, α)$

References

Template:Eom

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

@@ Line 1: / Line 1: @@
-One point kitchen knives shouldn't be is just "ordinary." Don't forget a knife is a single of the most fundamental pieces of gear in your kitchen, so make positive that your knives are of most effective high quality you can afford.  Welcome to !  Are you a cook?  If you loved this article and you wish to receive more details relating to [http://www.thebestkitchenknivesreviews.com/wusthof-knives-review-single-brand-different-choices/ Wusthof Hunting Knives Assessment] assure visit our site. If you are concerned to acquire this knife sharpener make certain to pick the [http://www.Answers.com/topic/genuine genuine] one particular from reliable shops. Your fork must be strong and at least 16 inches lengthy and be accompanied by a fantastic chef or butcher type knife.  Aluminium cookware, stainless cookware, fry pans, iron wok , rice cookers, flatware set and even additional.  New for 2012 are a set of knives especially developed for females.<br><br><br><br>The OXO Superior Grips 14 piece knife set gives a wide array of the most well-known type of knives employed in the total the 14 knives set boasts of 6 prep knives, one Santoku, eight Inch bread knife, one eight inch lengthy chef knife, six steak knives, a [http://www.alexa.com/search?q=sharpening+block&r=topsites_index&p=bigtop sharpening block] or tool and a wood storage block with an angled face for simple accessibility. In addition, each and every knife delivers a full tang that runs the complete length escalating balance and durability.<br><br>The 8-inch Chef's knife is a multipurpose knife from Victorinix which is designed for chopping, mincing, slicing, and dicing.  This Chef's knife is a preferred with experienced Chefs and culinary students due to its affordability and hygienic building. This is a excellent knife for tackling these daily kitchen tasks, it's smaller, lighter and agile adequate to be utilised for paring, intricate peeling jobs and is also massive enough to reduce, trim, and prep vegetables and fruit.<br><br>The Paring knife is valuable to have in the kitchen due to the fact it is able to total frequent knife connected tasks such as deveining shrimp, deseeding jalapenos, as well as cutting compact quantities of garnish.  The Petty knife is very handy for when you need to have to slice soft vegetables that are light in weight such as the string beans, onions and other medium size vegetables.  The Boning knife is commonly what is utilized for boning fish, poultry and meat.<br><br>An eight-inch knife is easy for cutting fruits and vegetables, and will peel and slice as effectively as chop items like herbs.  A nicely-balanced French knife is comfortable to deal with, maneuvers quickly in small spaces and does just about anything essential for a swift meal prep. A very good knife will final a lengthy time if you never throw it in the drawer when you're completed cutting.  A chef's knife must really feel balanced in you hand.<br><br>A lightweight knife is excellent for speed and precision, whereas a heavy knife demands extra perform when chopping a lot of light ingredients.  To test the balance, spot your finger at the finger grip at the hilt or blade-end of the manage, holding the knife horizontally with the cutting edge down.  A excellent, properly balanced knife will balance at that point and not fall off your finger. Any knife or any sharp blade instrument is unsafe.<br><br>Some evaluations evaluate these knives to a $500 set from Henckels and Shoppers Digest selected these over lots of sets costing hundreds ofmore (including a Mundial set that they reviewed). Having said that, there is a set of steak knives that could possibly serve you well in various strategies in your kitchen.  This Chicago Cutlery Steak Knife Set is really appealing for each day use or on unique occasions.  They appear like and will compliment the Chicago Cutlery Fusion set above.  But, a kitchen set has weakness.<br><br>In addition, noteworthy to make mention are three feasible solutions on how to hone a knife like the sharpening making use of a whetstone, honing making use of a grinder, and honing making use of a sharpening steel. This guide ahead of will showcase some of the best and most economical knife sets for 2012 no lies. The chef kitchen knife which appears to the left is your bread and butter when it comes to cutting something.<br><br>If you nevertheless want a standard knife block appear for one particular that stores the knives on their sides rather than sliding the knife in on its blade edge. My much less high-priced knives I use my series of scanpan and bodum soft touch knife blocks, a single for clean knves and the other for dirty knives.  According to America's Test Kitchen (which is the last word, in my opinion) the Victorinox Chef's Knife is the greatest chef's knife out there.
+{{Probability distribution |
+  name       =Arcsine|
+  type       =density|
+  pdf_image  =[[Image:Arcsin density.svg|350px|Probability density function for the arcsine distribution]]|
+  cdf_image  =[[Image:Arcsin cdf.svg|350px|Cumulative distribution function for the arcsine distribution]]|
+  parameters =none|
+  support    =<math>x \in [0,1]</math>|
+  pdf        =<math>f(x) = \frac{1}{\pi\sqrt{x(1-x)}}</math> |
+  cdf        =<math>F(x) = \frac{2}{\pi}\arcsin\left(\sqrt x \right)</math> |
+  mean       =<math>\frac{1}{2}</math> |
+  median     =<math>\frac{1}{2}</math> |
+  mode       =<math>x \in {0,1}</math> |
+  variance   =<math>\tfrac{1}{8}</math> |
+  skewness   =<math>0</math>|
+  kurtosis   =<math>-\tfrac{3}{2}</math>|
+  entropy    = |
+  mgf        = <math>1  +\sum_{k=1}^{\infty} \left( \prod_{r=0}^{k-1} \frac{2r+1}{2r+2} \right) \frac{t^k}{k!}</math>|
+  char       = <math>{}_1F_1(\tfrac{1}{2}; 1; i\,t)\ </math>|
+}}
+In [[probability theory]], the '''arcsine distribution''' is the [[probability distribution]] whose [[cumulative distribution function]] is
+:<math>F(x) = \frac{2}{\pi}\arcsin\left(\sqrt x\right)=\frac{\arcsin(2x-1)}{\pi}+\frac{1}{2}</math>
+for 0&nbsp;≤&nbsp;''x''&nbsp;≤&nbsp;1, and whose probability density function is
+:<math>f(x) = \frac{1}{\pi\sqrt{x(1-x)}}</math>
+on&nbsp;(0,&nbsp;1).  The standard arcsine distribution is a special case of the [[beta distribution]] with ''&alpha;''&nbsp;=&nbsp;''&beta;''&nbsp;=&nbsp;1/2. That is, if <math>X</math> is the standard arcsine distribution then <math>X \sim {\rm Beta}(\tfrac{1}{2},\tfrac{1}{2}) \ </math>
+The arcsine distribution appears
+* in the [[Lévy arcsine law]];
+* in the [[Erdős arcsine law]];
+* as the [[Jeffreys prior]] for the probability of success of a [[Bernoulli trial]].
+==Generalization==
+{{Probability distribution |
+  name       =Arcsine – bounded support|
+  type       =density|
+  pdf_image  = Need image|
+  cdf_image  = Need image|
+  parameters =<math>-\infty < a < b < \infty \,</math>|
+  support    =<math>x \in [a,b]</math>|
+  pdf        =<math>f(x) = \frac{1}{\pi\sqrt{(x-a)(b-x)}}</math> |
+  cdf        =<math>F(x) = \frac{2}{\pi}\arcsin\left(\sqrt \frac{x-a}{b-a} \right)</math> |
+  mean       =<math>\frac{a+b}{2}</math> |
+  median     =<math>\frac{a+b}{2}</math> |
+  mode       =<math>x \in {a,b}</math> |
+  variance   =<math>\tfrac{1}{8}(b-a)^2</math> |
+  skewness   =<math>0</math>|
+  kurtosis   =<math>-\tfrac{3}{2}</math>|
+  entropy    = |
+  mgf        = |
+  char       = |
+}}
+===Arbitrary bounded support===
+The distribution can be expanded to include any bounded support from ''a''&nbsp;≤&nbsp;''x''&nbsp;≤&nbsp;''b'' by a simple transformation
+:<math>F(x) = \frac{2}{\pi}\arcsin\left(\sqrt \frac{x-a}{b-a} \right)</math>
+for ''a''&nbsp;≤&nbsp;''x''&nbsp;≤&nbsp;''b'', and whose [[probability density function]] is
+:<math>f(x) = \frac{1}{\pi\sqrt{(x-a)(b-x)}}</math>
+on&nbsp;(''a'',&nbsp;''b'').
+===Shape factor===
+The generalized standard arcsine distribution on (0,1) with probability density function
+:<math>
+\begin{align}
+f(x;\alpha) & = \frac{\sin \pi\alpha}{\pi}x^{-\alpha}(1-x)^{\alpha-1} \\[6pt]
+\end{align}
+</math>
+is also a special case of the [[beta distribution]] with parameters <math>{\rm Beta}(1-\alpha,\alpha)</math>.
+Note that when <math>\alpha = \tfrac{1}{2}</math> the general arcsine distribution reduces to the standard distribution listed above.
+==Properties==
+* Arcsine distribution is closed under translation and scaling by a positive factor
+** If  <math>X \sim {\rm Arcsine}(a,b) \  \text{then }  kX+c \sim {\rm Arcsine}(ak+c,bk+c) </math>
+* The square of an arc sine distribution over (-1, 1) has arc sine distribution over (0, 1)
+** If  <math>X \sim {\rm Arcsine}(-1,1) \  \text{then }  X^2 \sim {\rm Arcsine}(0,1) </math>
+==Related distributions==
+* If U and V are [[Independent and identically distributed random variables|i.i.d]] [[Uniform distribution (continuous)|uniform]] (−π,π) random variables, then <math>\sin(U)</math>, <math>\sin(2U)</math>, <math>-\cos(2U)</math>, <math>\sin(U+V)</math> and <math>\sin(U-V)</math> all have a standard arcsine distribution
+* If <math>X</math> is the generalized arcsine distribution with shape parameter <math>\alpha</math> supported on the finite interval [a,b] then  <math>\frac{X-a}{b-a} \sim {\rm Beta}(1-\alpha,\alpha) \ </math>
+==See also==
+* [[Arcsine]]
+==References==
+*{{eom|id=A/a013160|first=B.A.|last= Rogozin}}
+{{ProbDistributions|continuous-bounded}}
+{{Common univariate probability distributions}}
+[[Category:Continuous distributions]]
+[[Category:Probability distributions]]

Energy operator: Difference between revisions

Revision as of 17:28, 5 December 2013

Contents

Generalization

Arbitrary bounded support

Shape factor

Properties

Related distributions

See also

References

Navigation menu

Energy operator: Difference between revisions

Revision as of 17:28, 5 December 2013

Generalization

Arbitrary bounded support

Shape factor

Properties

Related distributions

See also

References

Navigation menu

Search