Dagum distribution
Encyclopedia
The Dagum distribution is a continuous probability distribution
defined over all positive real numbers. It is named after Camilo Dagum, who proposed it in a series of papers in the 1970s. The Dagum distribution arose from several variants of a new model on the size distribution of personal income and is mostly associated with the study of income distribution
. There is both a three-parameter specification (Type I) and a four-parameter specification (Type II) of the Dagum distribution; a summary of the genesis of this distribution can be found in. A general source on statistical size distributions often cited in work using the Dagum distribution is.
of the Dagum distribution (Type I) is given by
for 
and where 
The corresponding probability density function
is given by
The Dagum distribution can be derived as a special case of the generalized Beta II (GB2) distribution. There is also an intimate relationship between the Dagum and Singh-Maddala distribution.
The cumulative distribution function
of the Dagum (Type II) distribution adds a point mass at the origin and then follows a Dagum (Type I) distribution over the rest of the support (i.e. over the positive halfline)
Probability distribution
In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....
defined over all positive real numbers. It is named after Camilo Dagum, who proposed it in a series of papers in the 1970s. The Dagum distribution arose from several variants of a new model on the size distribution of personal income and is mostly associated with the study of income distribution
Income distribution
In economics, income distribution is how a nation’s total economy is distributed amongst its population.Income distribution has always been a central concern of economic theory and economic policy...
. There is both a three-parameter specification (Type I) and a four-parameter specification (Type II) of the Dagum distribution; a summary of the genesis of this distribution can be found in. A general source on statistical size distributions often cited in work using the Dagum distribution is.
Definition
The cumulative distribution functionCumulative distribution function
In probability theory and statistics, the cumulative distribution function , or just distribution function, describes the probability that a real-valued random variable X with a given probability distribution will be found at a value less than or equal to x. Intuitively, it is the "area so far"...
of the Dagum distribution (Type I) is given by
for and where The corresponding probability density function
Probability density function
In probability theory, a probability density function , or density of a continuous random variable is a function that describes the relative likelihood for this random variable to occur at a given point. The probability for the random variable to fall within a particular region is given by the...
is given by
The Dagum distribution can be derived as a special case of the generalized Beta II (GB2) distribution. There is also an intimate relationship between the Dagum and Singh-Maddala distribution.
The cumulative distribution function
Cumulative distribution function
In probability theory and statistics, the cumulative distribution function , or just distribution function, describes the probability that a real-valued random variable X with a given probability distribution will be found at a value less than or equal to x. Intuitively, it is the "area so far"...
of the Dagum (Type II) distribution adds a point mass at the origin and then follows a Dagum (Type I) distribution over the rest of the support (i.e. over the positive halfline)
External links
- Camilo Dagum (1925 - 2005) : obituary