definition of Wikipedia
Advertizing ▼
Probability density function 

Cumulative distribution function 

Parameters  shape , rate (real) alt.: scale (real) 

Support  
CDF  
Mean  
Median  No simple closed form 
Mode  for 
Variance  
Skewness  
Ex. kurtosis  
Entropy  
MGF  for 
CF 
The Erlang distribution is a continuous probability distribution with wide applicability primarily due to its relation to the exponential and Gamma distributions. The Erlang distribution was developed by A. K. Erlang to examine the number of telephone calls which might be made at the same time to the operators of the switching stations. This work on telephone traffic engineering has been expanded to consider waiting times in queueing systems in general. The distribution is now used in the fields of stochastic processes and of biomathematics.
Contents 
The distribution is a continuous distribution, which has a positive value for all real numbers greater than zero, and is given by two parameters: the shape , which is a nonnegative integer, and the rate , which is a nonnegative real number. The distribution is sometimes defined using the inverse of the rate parameter, the scale . It is the distribution of the sum of independent exponential variables with mean .
When the shape parameter equals 1, the distribution simplifies to the exponential distribution. The Erlang distribution is a special case of the Gamma distribution where the shape parameter is an integer. In the Gamma distribution, this parameter is not restricted to the integers.
The probability density function of the Erlang distribution is
The parameter is called the shape parameter and the parameter is called the rate parameter. An alternative, but equivalent, parametrization uses the scale parameter which is the reciprocal of the rate parameter (i.e., ):
When the scale parameter equals 2, then distribution simplifies to the chisquared distribution with 2k degrees of freedom. It can therefore be regarded as a generalized chisquared distribution.
Because of the factorial function in the denominator, the Erlang distribution is only defined when the parameter k is a positive integer. In fact, this distribution is sometimes called the Erlangk distribution (e.g., an Erlang2 distribution is an Erlang distribution with k=2). The Gamma distribution generalizes the Erlang by allowing to be any real number, using the gamma function instead of the factorial function.
The cumulative distribution function of the Erlang distribution is:
where is the lower incomplete gamma function. The CDF may also be expressed as
Events that occur independently with some average rate are modeled with a Poisson process. The waiting times between k occurrences of the event are Erlang distributed. (The related question of the number of events in a given amount of time is described by the Poisson distribution.)
The Erlang distribution, which measures the time between incoming calls, can be used in conjunction with the expected duration of incoming calls to produce information about the traffic load measured in Erlang units. This can be used to determine the probability of packet loss or delay, according to various assumptions made about whether blocked calls are aborted (Erlang B formula) or queued until served (Erlang C formula). The ErlangB and C formulae are still in everyday use for traffic modeling for applications such as the design of call centers.
A.K. Erlang worked a lot in traffic modeling. There are thus two other Erlang distributions, both used in modeling traffic:
Erlang B distribution: this is the easier of the two, and can be used, for example, in a call centre to calculate the number of trunks one need to carry a certain amount of phone traffic with a certain "target service".
Erlang C distribution: this formula is much more difficult and is often used, for example, to calculate how long callers will have to wait before being connected to a human in a call centre or similar situation.
The Erlang distribution is the distribution of the sum of k independent identically distributed random variables each having an exponential distribution. The longrun rate at which events occur is the reciprocal of the expectation of , that is . The (age specific event) rate of the Erlang distribution is, for , monotonic in , increasing from zero at , to as tends to infinity.^{[1]}

sensagent's content
Dictionary and translator for handheld
New : sensagent is now available on your handheld
Advertising ▼
Webmaster Solution
Alexandria
A windows (popinto) of information (fullcontent of Sensagent) triggered by doubleclicking any word on your webpage. Give contextual explanation and translation from your sites !
SensagentBox
With a SensagentBox, visitors to your site can access reliable information on over 5 million pages provided by Sensagent.com. Choose the design that fits your site.
Business solution
Improve your site content
Add new content to your site from Sensagent by XML.
Crawl products or adds
Get XML access to reach the best products.
Index images and define metadata
Get XML access to fix the meaning of your metadata.
Please, email us to describe your idea.
Lettris
Lettris is a curious tetrisclone game where all the bricks have the same square shape but different content. Each square carries a letter. To make squares disappear and save space for other squares you have to assemble English words (left, right, up, down) from the falling squares.
boggle
Boggle gives you 3 minutes to find as many words (3 letters or more) as you can in a grid of 16 letters. You can also try the grid of 16 letters. Letters must be adjacent and longer words score better. See if you can get into the grid Hall of Fame !
English dictionary
Main references
Most English definitions are provided by WordNet .
English thesaurus is mainly derived from The Integral Dictionary (TID).
English Encyclopedia is licensed by Wikipedia (GNU).
Copyrights
The wordgames anagrams, crossword, Lettris and Boggle are provided by Memodata.
The web service Alexandria is granted from Memodata for the Ebay search.
The SensagentBox are offered by sensAgent.
Translation
Change the target language to find translations.
Tips: browse the semantic fields (see From ideas to words) in two languages to learn more.
last searches on the dictionary :
computed in 0.046s