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[http://sss.chaoslab.ru/tracker/mim_plugs/newticket?reporter=anonymous&summary=AttributeError%3A+%27Environment%27+object+has+no+attribute+%27get_db_cnx%27&description=Swiss+Army+knives+have+been+around+for+nicely+over+a+century+and+it+seems+most+of+us+have+owned+at+the+least+one+one+at+some+point+in+our+lives.+The+Swiss+Military+knife+was+first+launched+and+manufactured+by+Wenger+as+a+part+of+a+contract+to+supply+knives+for+the+Swiss+Military+again+within+the+late+1800%E2%80%B2s.+In+1908+the+Swiss+Army+selected+to+offer+a+few+of+the+enterprise+to+another+manufacturer%2C+Victorinox+who+quickly+turned+a+competitor+to+Wenger.%0D%0A%0D%0AThe+soldier+Knife+model+1951+had+fiber+scales%2C+nickle-silver+bolsters%2C+liners%2C+and+divider%2C+and+a+spear+level+blade.+This+was+the+primary+Swiss+Armed+Forces+problem+mannequin+the+place+the+instruments+had+been+fabricated+from+chrome+steel.+The+screwdriver+now+had+a+scraper+arc+on+one+edge.+The+knife+was+ninety+three%C2%A0mm+%28three.7%C2%A0in%29+lengthy%2C+thirteen.5%C2%A0mm+%28zero.53%C2%A0in%29+mm+thick+and+weighed+ninety%C2%A0g+%28three.2%C2%A0oz%29.+Soldier+knife+model+1961++edit+The+Soldier+Knife+08+was+first+issued+to+the+Swiss+Armed+Forces+starting+with+the+first+primary+coaching+periods+of+2009.++30+When+touring%2C+my+Swiss+Military+Knife+is+the+equal+of+having+a+complete+tool+equipment+at+hand%2C+helpful+for+minor+automobile+repairs%2C+or+for+opening+a+can+of+tuna+and+reducing+via+a+block+of+cheese.+Piece+International+Knife+Set+%24744.ninety+five+%28provides+12+in.+Ceramic+Steel%29%0D%0A%0D%0AThere+are+a+lot+of+related+manufacturers+that+produces+an+identical+knives+from+these+well-known+products.+Many+customer+get+fooled+with+the+similar+looking+knivesThat%27s+why+you+have+to+be+very+cautious+when+%5Bhttp%3A%2F%2FBrowse.Deviantart.com%2F%3Fq%3Dchoosing+choosing%5D+these+items.+The+imitator+can+copy+the+design+however+you+possibly+can+identify+the+brand+based+on+their+quality.+It+is+best+to+avoid+being+tricked+by+some+manufacturers+if+you+happen+to+plan+to+purchase+low-cost+knives.+There+are+several+things+that+you+could+think+about+before+planning+to+buy+the+final+one.+Things+to+Examine+before+Buying+Swiss+Military+Knife%0D%0A%0D%0APiece+International+Knife+Set+%24874.95+%28adds+GS-9+Tomato+Knife+%2B+GSF-46+Paring+Knife+%2B+GTF-30+Cheese+Knife+%2B+12+in.+Ceramic+Metal%29+Bakers+Supplies%21+Click+on+Right+here%21+Our+new+unique+International+2+piece+set+contains+a+8+inch+blade+World+Chef+Knife%2C+essentially+the+most+used+knife+and+a+2.+If+you+have+any+questions+pertaining+to+exactly+where+and+how+to+use+%5Bhttp%3A%2F%2Fwww.thebestpocketknifereviews.com%2Fvictorinox-knives-review%2F+Victorinox+Fully+Forged+Knives+Review%5D%2C+you+can+get+hold+of+us+at+our+web+site.+5+in+Sheep+Foot+Paring+knife%21+Each+handmade+knife+is+solid+from+super+top+quality+Japanese+alloy+steel.+It+is+extremely+sharp.+Lifetime+Guarantee.+This+is+the+new+eight+3%2F4+inch+serrated+blade+Global+Bread+Knife%2C+%2822+cm%29+it+simply+glide+through+crusty+bread%2C+cakes%2C+sandwiches+and+more%21+Every+handmade+knife+is+forged+from+tremendous+prime+quality+Japanese+alloy+metal.+It+is+extremely+sharp.+Lifetime+Warranty.+Messermeister+Meridian+Elite+10-Inch+Kullenschliff+Chefs+Knife+%2C+%24142.seventy+three+from+Amazon+Sturdy%2C+robust+cast+steel%0D%0A%0D%0AGet+pleasure+from+no+payments+for+6+months.+You+may+have+6+months+with+no+funds%2C+and+no+curiosity+if+paid+in+full+inside+6+months+on+orders+over+%24250.+In+any+other+case%2C+interest+will+probably+be+charged+from+the+original+date+of+purchase.+Invoice+Me+Later+is+the+quick%2C+simple%2C+safe+approach+to+purchase+on-line+with+out+using+your+bank+card.+Simply+choose+Invoice+Me+Later+at+checkout.+Subject+to+credit+score+approval.+This+doc+shows+a+really+low+yield+power%2C+220+ksi%2C+much+decrease+thanhardened+cutlery+metal%2C+and+a+low+hardness%2C+about+50+HRC%2C+and+fairly+brittlenature.+The+density+can+be+much+decrease+than+metal%2C+6.three+g%2Fcm%5E2+vs+7.8-8.1+%5E3.%0D%0A%0D%0AIt+comes+with+a+polished+cellidor+case.+The+scissors+are+nice+for+paper+to+private+grooming%2C+the+tweezers%2C+large+screwdriver%2C+can+opener+are+largely+for+prying.+The+pillar+wire+cutter+is+awesome+that+can+be+utilized+to+chop+the+wire+protect.+Massive+clip+level+knife+blade+and+small+clip+level+knife+blade+are+really+sharp%2C+I%27m+not+kidding%2C+please+be+careful+when+you+deal+with+it.+The+multi+instrument+has+a+very+powerful+magnifying+glass.+When+you+don%27t+have+any+writing+instrument+then+you+can+use+Mini+pen%2C+it+writes+decently%2C+the+refill+is+cheap.+This+makes+a+fantastic+reward+on+your+family+members.+Highly+advocate%21%0D%0A%0D%0AParing+Knife+by+Victorinox+Swiss+Military+Paring+and+Peeling+Knives+What+Do+Individuals+Dislike+About+On-line+Shopping%3F+If+you%27re+on+the+lookout+for+Paring+Knife+by+Victorinox+Swiss+Army+Paring+and+Peeling+Knives+featuring+greater+than+anyone+else+to+use+class%2C+together+with+the+various+talents+Paring+Knife+by+Victorinox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crevasses] within the knife’s lock that lint loves to cover of their, and two times it built up enough to stop the lock from participating.<br><br>If this is your first knife, don’t get too hung up on the metal types used. 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{{Probability distribution
  | name      = Logit-normal
  | type      = continuous
  | pdf_image = [[Image:LogitnormalPDF.svg|325px|Plot of the Logitnormal PDF]]
  | cdf_image = [[Image:LogitnormCdfGrid2.svg|325px|Plot of the Logitnormal PDF]]
  | notation  = <math>P( \mathcal{N}(\mu,\,\sigma^2) )</math>
  | parameters= ''σ''<sup>2</sup> > 0 — squared scale (real),<br /> ''μ'' ∈ '''R''' — location
  | support  = ''x'' ∈ (0, 1)
  | pdf      = <math>\frac{1}{\sigma \sqrt{2 \pi}}\, e^{-\frac{(\operatorname{logit}(x) - \mu)^2}{2\sigma^2}}\frac{1}{x (1-x)}</math>
  | cdf      = <math>\frac12\Big[1 + \operatorname{erf}\Big( \frac{\operatorname{logit}(x)-\mu}{\sqrt{2\sigma^2}}\Big)\Big]</math>
  | mean      = no analytical solution
  | median    = <math>P(\mu)\,</math>
  | mode      = no analytical solution
  | variance  = no analytical solution
  | skewness  =
  | kurtosis  =
  | entropy  =
  | mgf      = no analytical solution
  | char      =
  | fisher    =  
  }}
 
In [[probability theory]], a '''logit-normal distribution''' is a [[probability distribution]] of a [[random variable]] whose [[logit]] has a [[normal distribution]]. If ''Y'' is a random variable with a normal distribution, and ''P'' is the [[logistic function]], then ''X''&nbsp;=&nbsp;''P''(''Y'') has a logit-normal distribution; likewise, if ''X'' is logit-normally distributed, then ''Y''&nbsp;=&nbsp;[[logit]](''X'')= log (''X''/(1-''X'')) is normally distributed. It is also known as the '''logistic normal distribution''',<ref>J Atchison and SM Shen.  "Logistic-normal distributions: Some properties and uses."  Biometrika, 1980. [http://scholar.google.com/scholar?q=aitchison%20logistic%20normal Google Scholar link]</ref> which often refers to a multinomial logit version (e.g. <ref>http://people.csail.mit.edu/tomasz/papers/huang_hln_tech_report_2006.pdf</ref> <ref>Peter Hoff, 2003. [http://www.stat.washington.edu/hoff/Preprints/nhed.ps Link]</ref> <ref>http://www.springerreference.com/docs/html/chapterdbid/205424.html</ref> <ref>http://brenocon.com/blog/2011/05/log-normal-and-logistic-normal-terminology/</ref>).
 
A variable might be modeled as logit-normal if it is a proportion, which is bounded by zero and one, and where values of zero and one never occur.
 
== Characterization ==
 
=== Probability density function ===
The [[probability density function]] of a logit-normal distribution is:
 
: <math>f_X(x;\mu,\sigma) = \frac{1}{\sigma \sqrt{2 \pi}}\, e^{-\frac{(\operatorname{logit}(x) - \mu)^2}{2\sigma^2}} \frac{1}{x (1-x)},  \quad x \in (0, 1) </math>
 
where ''μ'' and ''σ'' are the [[mean]] and [[standard deviation]] of the variable’s [[logit]] (by definition, the variable’s logit is normally distributed).
 
[[Image:LogitnormDensityGrid.svg|630px|Plot of the Logitnormal PDF for various combinations of ''μ'' (facets) and ''σ'' (colors)]]
 
The density obtained by changing the sign of ''μ'' is symmetrical, in that it is equal to f(1-x;-''μ'',''σ''), shifting the mode to the other side of 0.5 (the midpoint of the (0,1) interval).
 
=== Moments ===
The moments of the logit-normal distribution have no analytic solution. However, they can be
estimated by [[numerical integration]].
 
=== Mode ===
When the derivative of the density equals 0 then the location of the mode x satisfies the following equation:
 
:<math>\operatorname{logit}(x) = \sigma^2(2x-1)+\mu .</math>
 
== See also ==
* [[Beta distribution]] and [[Kumaraswamy distribution]], other two-parameter distributions on a bounded interval with similar shapes
 
== Further reading ==
* Frederic, P. & Lad, F. (2008) [http://www.economia.unimore.it/frederic_patrizio/Hidden/Papers/2008%20Frederic-Lad%20Comm%20Stat%20Revised.pdf Two Moments of the Logitnormal Distribution.] ''Communications in Statistics-Simulation and Computation''. 37: 1263-1269
* {{cite JSTOR|2528553}}
{{reflist}}
 
==External links==
* [http://logitnorm.r-forge.r-project.org/ logitnorm package] for [[R (programming language)|R]]
 
{{ProbDistributions|continuous-bounded}}
 
{{DEFAULTSORT:Logit-Normal Distribution}}
[[Category:Continuous distributions]]
[[Category:Probability distributions]]

Revision as of 02:41, 17 January 2014

Template:Probability distribution

In probability theory, a logit-normal distribution is a probability distribution of a random variable whose logit has a normal distribution. If Y is a random variable with a normal distribution, and P is the logistic function, then X = P(Y) has a logit-normal distribution; likewise, if X is logit-normally distributed, then Y = logit(X)= log (X/(1-X)) is normally distributed. It is also known as the logistic normal distribution,[1] which often refers to a multinomial logit version (e.g. [2] [3] [4] [5]).

A variable might be modeled as logit-normal if it is a proportion, which is bounded by zero and one, and where values of zero and one never occur.

Characterization

Probability density function

The probability density function of a logit-normal distribution is:

where μ and σ are the mean and standard deviation of the variable’s logit (by definition, the variable’s logit is normally distributed).

Plot of the Logitnormal PDF for various combinations of μ (facets) and σ (colors)

The density obtained by changing the sign of μ is symmetrical, in that it is equal to f(1-x;-μ,σ), shifting the mode to the other side of 0.5 (the midpoint of the (0,1) interval).

Moments

The moments of the logit-normal distribution have no analytic solution. However, they can be estimated by numerical integration.

Mode

When the derivative of the density equals 0 then the location of the mode x satisfies the following equation:

See also

Further reading

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