Modified Generalized Half-Normal Distribution with Application to Lifetimes

Olmos, Neveka M.; Venegas, Osvaldo

doi:10.18576/amis/120320

Cited by 3 publications

(3 citation statements)

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“…The standard probability distribution model [40][41][42] for estimating the probability of occurrence of an individual pixel within an image is given by Equation (11).…”

Section: Mathematical Modelling Of the Proposed Algorithmmentioning

confidence: 99%

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Conversion of Landsat 8 multispectral data through modified private content‐based image retrieval technique for secure transmission and privacy

Shakya

Ramola

Vidyarthi

2020

Engineering Reports

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In this research work, we have developed a new image encryption-based algorithm for Landsat 8 satellite images. Image statistical parameters related to first-order image statistics, that is, mean (μ), SD (σ), and variance (σ 2) are used to obtain the feature values for both original images and their encrypted versions. Multispectral satellite images generally contain a wide range of bands, which is 9 to 11 specifically for the Landsat 8 satellite. Hence, the information content of these images is richer than typical images. Through this algorithm, we aim to reduce the image content by randomly selecting only 10% of the total image pixels. These pixels are used to create new images, the so-called encrypted images. The visual presentation of the encrypted image resembles a noisy picture. First-order image statistics are calculated for both original images and their encrypted counterparts. These parameters show a similarity in their numerical values for both original and encrypted images. Thus, noisy pictures can be used for transmission in place of the original image when an outcome is decided through statistical image features. The visual similarity in the original images and encrypted images is obtained from the histogram signature plot for both original and encrypted images. The proposed algorithm can hence be used to convert image data for secure transmission and privacy.

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“…The standard probability distribution model [40][41][42] for estimating the probability of occurrence of an individual pixel within an image is given by Equation (11).…”

Section: Mathematical Modelling Of the Proposed Algorithmmentioning

confidence: 99%

“…The standard probability distribution model 40‐42 for estimating the probability of occurrence of an individual pixel within an image is given by Equation (11).

f (\frac{x}{μ}, σ^{2}) = \frac{1}{\sqrt{2 π σ^{2}}} e^{- \frac{{false(x - μ false)}^{2}}{2 σ^{2}}},

where μ represents the mean or expectation of the normal distribution.…”

Section: Mathematical Modelling Of the Proposed Algorithmmentioning

confidence: 99%

Conversion of Landsat 8 multispectral data through modified private content‐based image retrieval technique for secure transmission and privacy

Shakya

Ramola

Vidyarthi

2020

Engineering Reports

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“…Elal-Olivero (2010) generated the Alpha-Skew-Normal (ASN) distribution, which has one asymmetric parameter. On the other side, Olmos and Venegas (2018) studied the Modified Generalized Half-Normal (MGHN) variable developed with the modulus of a ASN random variable, considering a scale parameter and a shape parameter. The Half-Alpha-Skew-Normal (HASN) distribution is another generalization of the HN distribution and was introduced in (Olmos and Venegas, 2018).…”

Section: Introductionmentioning

confidence: 99%

A Flexible Probability Model for Reliability Data Analysis: The Extended Half-Normal Distribution with Further Results

Khorsheed¹,

Salinas²,

Bakouch³

2022

KJS publishes peer-review articles in Mathematics, Computer Sci

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Recent years have shown growth in the potential applications of extensions of skew and half-normal distributions. In this paper, we provide and study, in detail, an extended class of such distributions. The presented distribution has a scale parameter and two shape parameters. The motivations behind the development of this distribution are: 1- the probability distribution function has skewed, unimodal and bathtub shapes with different styles and the hazard rate function is increasing with various shapes, which makes this distribution flexible enough to analyze reliability data; 2- it can be expressed as a mixture of the Generalized Half-Normal distribution and the new weighted Generalized Half-Normal distribution. A number of statistical results are derived. Monte Carlo simulation analysis is carried out with Maximum Likelihood Estimation to assess the performance of this technique for a variety of the distribution parameter values. The power of the distribution is demonstrated with real applications using two reliability datasets from the industry. The results reveal that the proposed distribution outperformed the Generalized Lindley, Exponentiated Exponential, Gamma, Alpha-Skew-Normal, the Half-Alpha- Skew-Normal, and the Modified Generalized Half-Normal distributions.

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