The Generalized Lambda Distribution Estimation and Goodness of Fit With application
Salah El-Din Afifi;
Abstract
The problem of fitting a probability distribution to a set of data is not an easy task, since there are often several closely competing distributions that can fit. One approach to fitting data is to
choose a general distribution family, and fit some form of it to the random sample on hand. A number of such families exist; among the earliest is the Pearson system, depending on differential equations (1976), the Burr system (1973), the Johnson system and the generalized Lambda distribution (Ramberg et al. 1972&1974).
The Generalized Lambda Distribution (GLD) is a simple and flexible distribution that can
assume a wide range of shapes and more importantly uses only one general formula. The OLD's simplicity (requires only matching the first four sample estimates to their OLD counterparts) and versatility in fitting a broad range of curve shapes, makes it an ideal candidate for further investigation.
The OLD, given its flexibility, has been intensively used to fit and model a wide variety of continuous data in different disciplines, to name some:
1. Generating random numbers (Stengos and Wu, 2006; Wilcox, 2002).
2. Simulation ofM\M\1 queue systems (Dengiz, 1988),
3. Statistical process control (control charts )(Fournier et al., 2006),
4. Meteorology( Fitting GLD to solar radiation) (Oztiirk and Dale, 1982),
5. Fitting income data (Tarsitano, 2004,2005),
6. Metal corrosion (to Predict the Pit Depth of a Corrosion Process) (Najjar et al., 2003), ,
7. Fatigue lifetime of materials (Bigerelle et al., 2005),
8. Independent component analysis (Eriksson et al., 2000; Karvanen et al., 2002),
9. Modeling flood frequency (Atiem et al. (2006), Asquith (2007), El-louze et al. (2008) , In fact many of the well-known distributions can be very well approximated using the OLD. This Research will review different parameterizations of the OLD and its different estimation methods, conduct a simulation study to compare these methods performance and finally utilize those results in conducting a case study application in an attempt to model the river Nile flood data.
choose a general distribution family, and fit some form of it to the random sample on hand. A number of such families exist; among the earliest is the Pearson system, depending on differential equations (1976), the Burr system (1973), the Johnson system and the generalized Lambda distribution (Ramberg et al. 1972&1974).
The Generalized Lambda Distribution (GLD) is a simple and flexible distribution that can
assume a wide range of shapes and more importantly uses only one general formula. The OLD's simplicity (requires only matching the first four sample estimates to their OLD counterparts) and versatility in fitting a broad range of curve shapes, makes it an ideal candidate for further investigation.
The OLD, given its flexibility, has been intensively used to fit and model a wide variety of continuous data in different disciplines, to name some:
1. Generating random numbers (Stengos and Wu, 2006; Wilcox, 2002).
2. Simulation ofM\M\1 queue systems (Dengiz, 1988),
3. Statistical process control (control charts )(Fournier et al., 2006),
4. Meteorology( Fitting GLD to solar radiation) (Oztiirk and Dale, 1982),
5. Fitting income data (Tarsitano, 2004,2005),
6. Metal corrosion (to Predict the Pit Depth of a Corrosion Process) (Najjar et al., 2003), ,
7. Fatigue lifetime of materials (Bigerelle et al., 2005),
8. Independent component analysis (Eriksson et al., 2000; Karvanen et al., 2002),
9. Modeling flood frequency (Atiem et al. (2006), Asquith (2007), El-louze et al. (2008) , In fact many of the well-known distributions can be very well approximated using the OLD. This Research will review different parameterizations of the OLD and its different estimation methods, conduct a simulation study to compare these methods performance and finally utilize those results in conducting a case study application in an attempt to model the river Nile flood data.
Other data
| Title | The Generalized Lambda Distribution Estimation and Goodness of Fit With application | Other Titles | لا يوجد | Authors | Salah El-Din Afifi | Issue Date | 2009 |
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