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We develop a new empirical Bayes analysis in multiple regression models. In the present work we consider multivariate skew normal as prior for coefficients of the model in a skew-normal population and give empirical Bayes estimation for parameters of the model. The marginal distribution of response is found to be a closed skew-normal distribution. The empirical Bayes estimator is found in a closed form and the model is applied on a data set.

Background and Aim: Different surgical techniques have been proposed for crown exposure among patients under orthodontic treatment. The aim of this study was to investigate periodontal indices in closed flap operation technique used for impacted teeth crown exposure.Materials and Methods: In this descriptive study (2001-2003) 20 patients (15 females and 5 males), age ranging from 15 to 20 years, were participated. Following the performance of closed flap operation technique, in 12 patients impacted canine and central incisors were exposed and treated orthodontically. Periodontal parameters including sulcular depth, width of keratinized gingiva and attachment loss were recorded. Results: The mean of gingival sulcus depth was 1.50±0.43, the means of keratinized gingival in central incisors and canines were 3.07±0.53 and 2.30±0.42, respectively. In one patient, attachment loss was reported.Conclusion: Considering the optimal sulcular depth and keratinized gingiva, the closed flap operation technique seems suitable.

In this paper, we provide the expectation of a function of the quadratic form of the multivariate skew Laplace distribution using the generalized Laguerre series that can be applied to compute the elements of the Fisher information matrix. Finally, we give a numerical example to obtain the expectation of this quadratic form.

Drought is a challenging problem that can be evaluated with multi-variable and combined perspectives. Therefore, the aim of this study is to create a comprehensive index of three indices SPI, PDSI, and SRI, which includes all aspects of meteorology, hydrology, and agriculture. For this purpose, three drought variables (severity, duration, Magnitude) were analyzed for 10 meteorological stations in Iran for the statistical period of 1990-2021, firstly using principal component analysis (PCA) and nonlinear coupling based on copula. were analyzed. The probability distribution model for constructing the MCDI composite index. It was then tested with the ability of the exact functions of Clayton, Frank, and Gamble to generate a trivariate joint distribution. The best copula function for each station was determined through the Kolmograf-Smirnov (K_S) test, and the results showed the superiority of the Gumbel function in most stations. Return period curves were drawn for all stations and for all three joints. The period of returns indicated a long-term frequency of drought with greater intensity for periods of 50 and 100 years. The shortest return period of 50 years with the superiority of Clayton's function related to Tabriz and with the superiority of Gumbel's function related to Tehran was 10 months and the longest period was 30 months related to Mashhad with the superiority of Gumbel's function, respectively with intensity of 6.53 and 8.95 and 26/34 were included. For the 100-year return period, the shortest period with the superiority of Clayton is related to Tabriz with 13 months and intensity of 13.75, and the longest period with the superiority of Gumbel's function belongs to Kerman with a duration of 48 months, and the intensity of 42.56. The results of this research show that the use of a multivariate composite index (MCDI) by using detailed functions provides the possibility of a more comprehensive and accurate assessment of drought on a national scale. This approach, taking into account the meteorological, hydrological, and agricultural aspects of drought, provides an efficient tool for managing water resources and strategic planning in the face of drought in different regions of Iran.

The exact distribution of many applicable statistics could not be accessible in various statistical inference problems. To deal with such an issue in the large sample problem, an approach is to obtain the asymptotic distribution. In this article, we have expressed the asymptotic distribution of multivariate statistics class approximated by averages based on the Taylor expansion. Then, the asymptotic distribution of an empirical Mahalanobis depth-based statistic is obtained, and the statistic is applied to test the scale difference between two multivariate distributions. Simulation studies are carried out to explore the behavior of the asymptotic distribution of the test statistic. A real data example illustrating the use of the test is also presented.

In order to determine the effect of climatic factors on the distribution of forest types in one of the western provinces of Iran, Charmahal, among 71 climatic elements effective in ecological conditions of forest species, 3 factors were selected using factor analysis method.The factors covering 91.82 percent of total variance included thermal temperature, rainfall and radiation. Finally, the effect of each factor as well as the primary climatic varieties on distribution of these species and the mean elevation of the plant types in each distribution class was determined. The results of factor analysis indicate that thermal temperature and rainfall are the most important factors in relation to distribution of forest species. Moreover it can be concluded that semi humid and moderate climatic zones are the best habitats for distribution of Quercus brantii and its associated species, which are the dominant forest types in Charmahal province. This study also suggests that the distribution of Quercus brantii and the appearance of Lonicera nummularrifolia and Amygdalus spp. have been controlled by increasing altitude and decreasing temperature. On the other hand, these two types are found in cold and dry mountainous regions. In conclusion, the selection of climatic variables related to ecological condition of species is important in determining the effects of climatic factors on the distribution of forest types in Charmahal province.

One of the obvious reasons for most disorders in network service provisioning is network path congestion. Congestion avoidance in today's networks is too costly and sometimes impossible. With the introduction of SDN, centralizing the equipment's control plane has become possible. This paper presents an enhanced method named ESV-DBRA to avoid congestion in multi-tenant SDN networks. At first, ESV-DBRA monitors the traffic load and delay of all network paths for each tenant individually. Then, by merging the parameters obtained from the monitoring, the Service Level Agreements (SLA), and a novel proposed cost function, it calculates the cost of the network paths per tenant. As a result, traffic for each tenant is routed through the path/paths at the lowest possible cost from the tenant's perspective. Next, the bandwidth quotas will be calculated and assigned to the tenants over their optimal routes. Afterward, whenever congestion is likely to occur in a path, ESV-DBRA automatically changes the route or bandwidth of the tenants' traffic related to this path to avoid congestion. Related algorithms are also proposed.Eventually, simulations show that the proposed method effectively increases bandwidth utilization by 10.76%.