Distance-based clustering methods categorize samples by optimizing a global criterion, finding ellipsoid clusters with roughly equal sizes. In contrast, density-based clustering techniques form clusters with arbitrary shapes and sizes by optimizing a local criterion. Most of these methods have several hyper-parameters, and their performance is highly dependent on the hyper-parameter setup. Recently, a Gaussian density Distance (GDD) approach was proposed to optimize local criteria in terms of distance and density properties of samples. GDD can find clusters with different shapes and sizes without any free parameters. However, it may fail to discover the appropriate clusters due to the interfering of clustered samples in estimating the density and distance properties of remaining unclustered samples. Here, we introduce Adaptive GDD (AGDD), which eliminates the inappropriate effect of clustered samples by adaptively updating the parameters during clustering. It is stable and can identify clusters with various shapes, sizes, and densities without adding extra parameters. The distance metrics calculating the dissimilarity between samples can affect the clustering performance. The effect of different distance measurements is also analyzed on the method. The experimental results conducted on several well-known datasets show the effectiveness of the proposed AGDD method compared to the other well-known clustering methods.

We discuss the classical efficiency criteria in density estimation and propose some variants. The context is a general density estimation scheme that contains the cases of i.i.d. or dependent random variables, in discrete or continuous time. Unbiased estimation, optimality and asymptotic optimality are considered. An example of a density estimator that satisfies some suggested criteria is given.

Sampling methods have a theoretical basis and should be operational in different forests; therefore selecting an appropriate sampling method is effective for accurate estimation of forest characteristics. The purpose of this study was to estimate the stand density (number per hectare) in Arasbaran forest using a variety of the plotless density estimators of the nearest neighbors sampling method includes the Closest Individual, the Nearest Neighbor, the Second Nearest Neighbor, the Compound, the Shared Point and the Continues Nearest Neighbor due to introducing the most suitable estimator for forests. For this purpose, all number of trees was counted per hectare (as control). Then, distances between random sampling points and five closest nearest neighboring trees were measured in a systematic randomized network. The density estimators were calculated in each method. The calculated value of the actual density was compared to estimators' values by the one sample t-test (p< 0. 05) method in the R software and based on the value of accuracy criterion. Finally, the tree spatial distribution pattern was calculated by Johnson-Zimmer and Hopkins indices. The results showed that the difference between all estimators value was significant (p≤ 0. 05) compared to the actual density (339. 5 N. ha1), except the Morisita and Cottam estimators in Closest Individual method, Byth and Ripley and Cottam & Curtis 1 estimators in Nearest Neighbor method and 4th and 5th neighbors estimators in Continuous Nearest Neighbor method. The results of the spatial distribution pattern showed the random distribution of trees in the study area. The performance evaluation of these estimators for other quantitative characteristics is recommended in the Arasbaran forest stands.

In order to map the forest canopy density Bivareh Ilam Landsat 8 satellite data of 22 July 2014 and FCD model was used. The FCD of four indicators of vegetation, soil, shade and the heat index by applying a suitable threshold was and the density of vegetation and forest canopy density map based on FCD in percent respectively. Forest density map obtained, according to the classes provided by the Supreme Council of Forest, Range and Soil of Forest and Rangeland and Watershed Management (7 classes) and a classification (5 classes), were defined. To determine the accuracy of the classified forest density map, a map of the ground reality of the images presented on the website of the Regional Centre spatial data infrastructure updates and spatial resolution are prepared. The highest overall accuracy and Kappa coefficient in the present study, the classification in five classes of 61.34% and 0.42, respectively, were calculated. The classification of 7 classes, the overall accuracy and kappa coefficient was estimated. Therefore we can conclude that in the Zagros forests, semi-massive to massive forest separation efficiency model is appropriate when the separation of the classes with lower density, is not accurate.

When the parametric model does not hold, and we cannot fit a parametric model to the data, the true density may be estimated non-parametrically, as in the case of a kernel estimate. The purpose of this paper is to present a comparison between parametric and non-parametric models. The parametric investigation contains Vuong's test, and tracking interval based on the known maximum likelihood estimation theory. The presented non-parametric analysis involves kernel density estimation. Modified differences of Kullback-Leibler criteria between two rival models and Vuong's test, have been considered. In this circumstance, we address the problem of cross-validation estimation of variance for Kullback-Leibler divergence between the true but unknown density and its kernel estimator. A simulation study and data analysis have shown that the parametric density is a more realistic estimate of the data generating density.

In this paper, the two-observational  percentile, percentile and maximum likelihood estimation of the probability density function of  Inverse Weibull random variable are studied. Finally, these estimates are compared using simulation studies and a real data.

One of the most important issues in inferential statistics is the existence of outlier observations. Since these observations have a great influence on fitted model and its related inferences, it is necessary to find a method for specifying the effect of outlier observations. The aim of this article is to investigate the effect of outlier observations on kernel density function estimation. In this article we have tried to represent a method for identification of outlier observations and their effect on kernel density function estimation by using forward search method.

Kernel method is one of the most common nonparametric density estimation and recently B-spline is used for estimation of a probability density function. These two methods in some how depend on selecting a smoothing parameter that has an important effect on precision of the estimators. In this paper, we consider kernel and B-spline methods of density estimation and smoothing parameter selection for these two methods. Then, the accuracy of the obtained estimators is compared by their mean square errors. Also, the effect of the number and dispersion of data on precision of estimators are studied. The results show that for a symmetric probability density, if the dispersion of data increases, the precision of both estimators decreases, while, for an asymmetric probability density function, the precision of the estimators increases for dispersion data.