Extended skew generalized normal distribution

Choudhury, K. S.; Matin, Mohammad A.

doi:10.1007/bf03263561

Cited by 19 publications

(8 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An extension58 of Eq. (24) using the marginal density from bivariate normal density function is defined as The skew normal distributions in Eqs (18) and (24) do not characterize the kurtosis of a distribution well and an extension that can characterize both skewness and kurtosis is proposed59 as Another extension60 based on normal distribution, which has the connection to normal order statistics, is where n is a positive integer and C n ( λ ) is given by When n is odd, C n ( λ ) can be expressed analytically as …”

Section: Methods For Generating Skewed Distributionsmentioning

confidence: 99%

See 1 more Smart Citation

Methods for generating families of univariate continuous distributions in the recent decades

Lee

Famoye

Alzaatreh

2013

WIREs Computational Stats

146

View full text Add to dashboard Cite

There has been a renewed interest in developing more flexible statistical distributions in recent decades. A major milestone in the methods for generating statistical distributions is undoubtedly the system of differential equation approach. There is a recent renewed interest in generating skewed distributions. Generally speaking, the methods developed prior to 1980s may be summarized into three categories: (1) method of differential equation, (2) method of transformation, and (3) quantile method. Techniques developed since 1980s may be categorized as ‘methods of combination’ for the reason that these methods attempt to combine existing distributions into new distributions or adding new parameters to an existing distribution. This article discusses five general methods of combination and their variations. These five are (1) method of generating skew distributions, (2) method of adding parameters (e.g., exponentiation), (3) beta generated method, (4) transformed‐transformer method, and (5) composite method. WIREs Comput Stat 2013, 5:219–238. doi: 10.1002/wics.1255 This article is categorized under: Algorithms and Computational Methods > Random Number Generation Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms Statistical and Graphical Methods of Data Analysis > Nonparametric Methods

show abstract

Section: Methods For Generating Skewed Distributionsmentioning

confidence: 99%

“…The skew normal distributions in Eqs (18) and (24) do not characterize the kurtosis of a distribution well and an extension that can characterize both skewness and kurtosis is proposed59 as …”

Section: Methods For Generating Skewed Distributionsmentioning

confidence: 99%

Methods for generating families of univariate continuous distributions in the recent decades

Lee

Famoye

Alzaatreh

2013

WIREs Computational Stats

146

View full text Add to dashboard Cite

show abstract

“…Assuming that the vibration signal of the transformer and the distribution of the vibration signal at different signal intervals are random makes it difficult to analyze the vibration signal trend. The cumulative probability distribution characteristics of the transformer vibration signal are analyzed because the cumulative probability distribution function can be used to observe the signal variation trend [26,27]. Figure 3 shows a difference in the cumulative probability distribution curves of the transformer vibration signal at various critical degrees of failure.…”

Section: Distribution Characteristics Of Transformer Vibration Signalsmentioning

confidence: 99%

Novel Transformer Fault Identification Optimization Method Based on Mathematical Statistics

Zhang

et al. 2019

Mathematics

View full text Add to dashboard Cite

Most power transformer faults are caused by iron core and winding faults. At present, the method that is most widely used for transformer iron core and winding faults identification is the vibration analysis method. The vibration analysis method generally determines the degree of fault by analyzing the energy spectrum of the transformer vibration signal. However, the noise reduction step in this method is complicated and costly, and the effect of denoising needs to be further improved to make the fault identification results more accurate. In addition, it is difficult to perform an accurate determination of the early mild failure of the transformer due to the effect of noise on the results. This paper presents a novel mathematical statistics method based on the vibration signal to optimize the vibration analysis method for the short-circuit failure of the transformer winding. The proposed method was used for linear analysis of the transformer vibration signal with different degrees of short-circuit failure of the transformer winding. By comparing the slope value of the transformer vibration signal cumulative probability distribution curve and analyzing the energy spectrum of the signal, the degree of short-circuit failure of the transformer winding was identified quickly and accurately. This method also simplified the signal denoising process in transformer fault detection, improved the accuracy of fault detection, reduced the time of fault detection, and provided good predictability for early mild faults of the transformer, thereby reducing the hidden hazards of operating the power transformer. The proposed optimization procedure offers a new research idea in transformer fault identification.

show abstract

“…The data was collected at the Australian Institute of Sport. It has been previously used and analyzed by (Jamalizadeh et al, 2011;Choudhury and Abdul Matin, 2011;Al-Aqtash et al, 2014). The data is as follows: 148.9, 149.0, 156.0, 156.9, 157.9, 158.9, 162.0, 162.0, 162.5, 163.0, 163.9, 165.0, 166.1, 166.7, 167.3, 167.9, 168.0, 168.6, 169.1, 169.8, 169.9, 170.0, 170.0, 170.3, 170.8, 171.1, 171.4, 171.4, 171.6, 171.7, 172.0, 172.2, 172.3, 172.5, 172.6, 172.7, 173.0, 173.3, 173.3, 173.5, 173.6, 173.7, 173.8, 174.0, 174.0, 174.0, 174.1, 174.1, 174.4, 175.0, 175.0, 175.0, 175.3, 175.6, 176.0, 176.0, 176.0, 176.0, 176.8, 177.0, 177.3, 177.3, 177.5, 177.5, 177.8, 177.9, 178.0, 178.2, 178.7, 178.9, 179.3, 179.5, 179.6, 179.6, 179.7, 179.7, 179.8, 179.9, 180.2, 180.2, 180.5, 180.5, 180.9, 181.0, 181.3, 182.1, 182.7, 183.0, 183.3, 183.3, 184.6, 184.7, 185.0, 185.2, 186.2, 186.3, 188.7, 189.7, 193.4, 195.9. The data is summarized in Table 3 and the performances of the competing distributions are given in Table 4.…”

Section: Data Set Imentioning

confidence: 99%

A Comparative Analysis on the Performance of the Convoluted Exponential Distribution and the Exponential Distribution in Terms of Flexibility

Owoloko¹,

Oguntunde²,

Adejumo³

2016

Journal of Mathematics and Statistics

View full text Add to dashboard Cite

Abstract:In this article, the convoluted exponential distribution which was derived as the sum of two independent exponentially distributed random variables was compared with the exponential distribution in terms of flexibility when applied to four real data sets. The idea is to verify if the convoluted exponential distribution would perform better than the exponential distribution in modeling real life situations. Some other basic statistical properties of the convoluted exponential distribution were also identified.

show abstract

Extended skew generalized normal distribution

Cited by 19 publications

References 9 publications

Methods for generating families of univariate continuous distributions in the recent decades

Methods for generating families of univariate continuous distributions in the recent decades

Novel Transformer Fault Identification Optimization Method Based on Mathematical Statistics

A Comparative Analysis on the Performance of the Convoluted Exponential Distribution and the Exponential Distribution in Terms of Flexibility

Contact Info

Product

Resources

About