Slow-growing hierarchy: Difference between revisions

Revision as of 14:40, 22 December 2013

The K-distribution is a probability distribution that arises as the consequence of a statistical or probabilistic model used in Synthetic Aperture Radar (SAR) imagery. The K distribution is formed by compounding two separate probability distributions, one representing the radar cross-section, and the other representing speckle that is a characteristic of coherent imaging.

The model used to represent the observed intensity X, involves compounding two gamma distributions. In each case a reparameterisation of the usual form of the family of gamma distributions is used, such that the parameters are:

the mean of the distribution, and
the usual shape parameter.

Density

The model is that X has a gamma distribution with mean σ and shape parameter L, with σ being treated as a random variable having another gamma distribution, this time with mean μ and shape parameter ν. The result is that X has the following density function (x > 0):^[1]

f_{X} (x; ν, L) = \frac{2}{x} {(\frac{L ν x}{μ})}^{\frac{L + ν}{2}} \frac{1}{Γ (L) Γ (ν)} K_{ν - L} (2 \sqrt{\frac{L ν x}{μ}}),

where K is a modified Bessel function of the second kind. In this derivation, the K-distribution is a compound probability distribution. It is also a product distribution:^[1] it is the distribution of the product of two independent random variables, one having a gamma distribution with mean 1 and shape parameter L, the second having a gamma distribution with mean μ and shape parameter ν.

This distribution derives from a paper by Jakeman and Pusey (1978).

Moments

The mean and variance are given^[1] by

E (X) = μ

var (X) = μ^{2} \frac{ν + L + 1}{L ν} .

Other properties

All the properties of the distribution are symmetric in L and ν.^[1]

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.

Sources

Redding, Nicholas J. (1999) Estimating the Parameters of the K Distribution in the Intensity Domain [1]. Report DSTO-TR-0839, DSTO Electronics and Surveillance Laboratory, South Australia. p. 60
Jakeman, E. and Pusey, P. N. (1978) "Significance of K-Distributions in Scattering Experiments", Physical Review Letters, 40, 546–550 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park.

@@ Line 1: / Line 1: @@
-If an existing Word - Press code is found vulnerable, Word - Press will immediately issue an update for that. Also, you may want to opt for a more professioanl theme if you are planning on showing your site off to a high volume of potential customers each day. Your parishioners and certainly interested audience can come in to you for further information from the group and sometimes even approaching happenings and systems with the church. Keep reading for some great Word - Press ideas you can start using today. Over a million people are using Wordpress to blog and the number of Wordpress users is increasing every day. <br><br>
+The '''K-distribution''' is a [[probability distribution]] that arises as the consequence of a statistical or probabilistic model used in [[Synthetic aperture radar|Synthetic Aperture Radar]] (SAR) imagery.  The K distribution is formed by [[Compound probability distribution|compounding]] two separate [[probability distribution]]s, one representing the [[radar cross-section]], and the other representing speckle that is a characteristic of coherent imaging.
-Always remember that an effective linkwheel strategy strives to answer all the demands of popular  search engines while reacting to the latest marketing number trends. Wordpress have every reason with it which promote wordpress development. It sorts the results of a search according to category, tags and comments. Being able to help with your customers can make a change in how a great deal work, repeat online business, and referrals you'll be given. Akismet is really a sophisticated junk e-mail blocker and it's also very useful thinking about I recieve many junk e-mail comments day-to-day across my various web-sites. <br><br>Usually, Wordpress owners selling the ad space on monthly basis and this means a residual income source.  If you beloved this article therefore you would like to collect more info about [http://blbuh.ru/wordpress_backup_plugin_325445 wordpress backup] i implore you to visit the web site. Note:  at a first glance WP Mobile Pro  themes do not appear to be glamorous or fancy. You've got invested a great cope of time developing and producing up the topic substance. These frequent updates have created menace in the task of optimization. If you've hosted your Word - Press website on a shared hosting server then it'll be easier for you to confirm the restricted access to your site files. <br><br>Google Maps Excellent navigation feature with Google Maps and latitude, for letting people who have access to your account Latitude know exactly where you are. The SEOPressor Word - Press SEO Plugin works by analysing each page and post against your chosen keyword (or keyword phrase) and giving a score, with instructions on how to improve it. Specialty about our themes are that they are easy to load, compatible with latest wordpress version and are also SEO friendly. Can you imagine where you would be now if someone in your family bought an original painting from van Gogh during his lifetime. See a product, take a picture, and it gives you an Amazon price for that product, or related products. <br><br>Every single module contains published data and guidelines, usually a lot more than 1 video, and when pertinent, incentive links and PDF files to assist you out. Being a Plugin Developer, it is important for you to know that development of Word - Press driven website should be done only when you enable debugging. As a result, it is really crucial to just take aid of some experience when searching for superior quality totally free Word - Press themes, Word - Press Premium Themes for your web site. Thus, Word - Press is a good alternative if you are looking for free blogging software. I have never seen a plugin with such a massive array of features, this does everything that platinum SEO and All In One SEO, also throws in the functionality found within SEO Smart Links and a number of other plugins it is essentially the swiss army knife of Word - Press plugins.
+The model used to represent the observed intensity ''X'', involves compounding two [[gamma distribution]]s. In each case a reparameterisation of the usual form of the family of gamma distributions is used, such that the parameters are:
+:*the mean of the distribution, and
+:*the usual shape parameter.
+==Density==
+The model is that ''X'' has a gamma distribution with mean ''σ'' and shape parameter ''L'', with ''σ'' being treated as a [[random variable]] having another gamma distribution, this time with mean ''μ'' and shape parameter ''ν''. The result is that ''X'' has the following density function (''x''&nbsp;>&nbsp;0):<ref name=Redding>Redding (1999)</ref>
+:<math>f_X(x;\nu,L)= \frac{2}{x} \left( \frac{L \nu x}{\mu} \right)^\frac{L+\nu}{2}
+      \frac{1}{\Gamma(L)\Gamma(\nu)}
+      K_{\nu-L} \left( 2 \sqrt{\frac{L \nu x}{\mu} } \right), </math>
+where ''K'' is a [[modified Bessel function]] of the second kind. In this derivation, the K-distribution is a [[compound probability distribution]]. It is also a [[product distribution]]:<ref name=Redding/> it is the distribution of the product of two independent random variables, one having a gamma distribution with mean 1 and shape parameter ''L'', the second having a gamma distribution with mean ''μ'' and shape parameter ''ν''.
+This distribution derives from a paper by Jakeman and Pusey (1978).
+==Moments==
+The mean and variance are given<ref name=Redding>Redding (1999)</ref> by
+:<math> \operatorname{E}(X)= \mu  </math>
+:<math> \operatorname{var}(X)= \mu^2 \frac{ \nu+L+1}{L \nu}  .</math>
+==Other properties==
+All the properties of the distribution are symmetric in  ''L'' and ''ν''.<ref name=Redding/>
+==Notes==
+{{Reflist}}
+==Sources==
+*Redding, Nicholas J. (1999) ''Estimating the Parameters of the K Distribution in the Intensity Domain''  [http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA368069]. Report DSTO-TR-0839, DSTO Electronics and Surveillance Laboratory, South Australia. p.&nbsp;60
+*Jakeman, E.  and Pusey, P. N. (1978) "Significance of K-Distributions in Scattering Experiments", ''Physical Review Letters'', 40, 546&ndash;550  {{doi|10.1103/PhysRevLett.40.546}}
+==Further reading==
+*Jakeman, E. (1980) "On the statistics of K-distributed noise", Journal of Physics A: Mathematics and General, 13, 31&ndash;48
+*Ward, K.D.; Tough, Robert J.A; Watts, Simon (2006) '' Sea Clutter: Scattering, the K Distribution and Radar Performance'', Institution of Engineering and Technology. ISBN 0-86341-503-2
+{{ProbDistributions|continuous-semi-infinite}}
+{{DEFAULTSORT:K-Distribution}}
+[[Category:Radar signal processing]]
+[[Category:Continuous distributions]]
+[[Category:Compound distributions]]
+[[Category:Probability distributions]]

Slow-growing hierarchy: Difference between revisions

Revision as of 14:40, 22 December 2013

Contents

Density

Moments

Other properties

Notes

Sources

Further reading

Navigation menu

Slow-growing hierarchy: Difference between revisions

Revision as of 14:40, 22 December 2013

Density

Moments

Other properties

Notes

Sources

Further reading

Navigation menu

Search