Discrete Generalized Inverted Exponential Distribution: Case Study Color Image Segmentation

Abstract

We present in this paper a discrete analogue of the continuous generalized inverted exponential distribution denoted by discrete generalized inverted exponential (DGIE) distribution. Since, it is cumbersome or difficult to measure a large number of observations in reality on a continuous scale in the area of reliability analysis. Yet, there are a number of discrete distributions in the literature; however, these distributions have certain difficulties in properly fitting a large amount of data in a variety of fields. The presented DGIE β , θ has shown the efficiency in fitting data better than some existing distribution. In this study, some basic distributional properties, moments, probability function, reliability indices, characteristic function, and the order statistics of the new DGIE are discussed. Estimation of the parameters is illustrated using the moment's method as well as the maximum likelihood method. Simulations are used to show the performance of the estimated parameters. The model with two real data sets is also examined. In addition, the developed DGIE is applied as color image segmentation which aims to cluster the pixels into their groups. To evaluate the performance of DGIE, a set of six color images is used, as well as it is compared with other image segmentation methods including Gaussian mixture model, K-means, and Fuzzy subspace clustering. The DGIE provides higher performance than other competitive methods.

Discrete Exponentiated Generalized Family of Distributions

“…Therefore, for any continuous distribution, it is possible to construct corresponding discrete distribution using (1). Many researchers used this approach to develop several discrete distributions.…”

“…In this subsection, the importance and applicability of the DE-ITL distribution is discussed by using two real data sets. The proposed distribution is compared with different competitive distributions such as discrete Marshall-Olkin inverted Topp-Leone (DMOITL) introduced by Almetwally et al [6], discrete Half Logistic (DHL) presented by Hegazy et al [23], discrete generalized inverted exponential (DGIE) proposed by AbdElaziz et al [1] and discrete generalized Rayleigh (DGR) obtained by Alamatsaz et al [3]. The fitted probability distributions are compared using some criteria, Akaike Information Criterion (AIC), Akaike Information Criterion with Correction (AICC), Bayesian Information Criterion (BIC) and Hannon-Quinn Information Criterion (HQIC).…”

“…It represents remission times, in weeks, for 20 leukemia patients randomly assigned to a specific treatment. The data is: 1,3,3,6,7,7,10,12,14,15,18,19,22,26,28,29,34,40,48,49. Table 4 presents the ML estimates and corresponding standard errors (SEs), p-value, −2lnL, AIC, BIC, AICC and HQIC.…”