Independence of observations is a fundamental assumption in designing an X chart for individual observations. But unfortunately, the assumption of existence of independent data is not even approximately satisfied. In fact, there is one kind of autocorrelation in the data. This paper demonstrates, through simulating an AR (1) process, that the autocorrelation in the data has deep effect on X chart. Moreover, estimators of standard deviation, mean moving range and median moving range to estimate process standard deviation are introduced. Among the cited estimators, the best of them is considered to estimate process standard deviation using autocorrelated data. Finally, two new estimators are presented to estimate process standard deviation using autocorrelated data.

Homogeneity of soil particles is the potent factor which affects soil spectral signatures and known as the Geometric Standard Deviation of soil particles (sg). This study presents the influence of sg on spectral studying of soil texture using four spectral data sets of LISSIII-P6 and was coincident sampling operations. Subsequent to satellite data preprocessing, some operations were done such as: Normalized Difference Vegetation Index, Principal Component Analysis, Soil Line Euclidean Distance and Unsupervised Classification on acquired data. By stratified randomized sampling method and according to the false color composite and protomorphic units of the main image of the study area, 95 sample points were eventually selected and gathered from 0-5cm of soil surface. Afterwards, geometric standard deviation (sg) and texture fragments were determined for each sample point in the soil lab. Samples were accordingly divided into two parts, on the basis of the computed geometric standard deviation: the first, sg<10 (homogeneous soil) and the second, sg³10 (heterogeneous soil). Subsequently via correlation operations for both group, it was expressly displayed which in the first group (sg<10), clay and sand had about 0.7-0.8 correlations with the remotely sensed data, whereas the second group (sg³10) had about 0-3-0.4. Hence, the geometric standard deviation (sg) of the study region can powerfully impress soil spectral reflectance.

In this paper, based on an appropriate pivotal quantity, two methods are introduced to determine confidence region for the mean and standard deviation in a two parameter uniform distribution, in which the application of numerical methods is not mandatory. In the first method, the smallest region is obtained by minimizing the confidence region’, s area, and in the second method, a simultaneous Bonferroni confidence interval is introduced by using the smallest confidence intervals. By the comparison of area and coverage probability of the introduced methods, as well as, comparison of the width of strip including the standard deviation in both methods, it has been shown that the first method has a better efficiency. Finally, an approximation for the quantile of F distribution used in calculating the confidence regions in a special case is presented.

Markowitz, in his Portfolio selection theory, stated that investors select their portfolios according to two criteria of risk and return. Accordingly, he presented his mathematical model. One of the criticisms of this model is that while investors, practically, consider different criteria in forming their portfolios, it only considers the return mean and return standard deviation. Liquidity is one of the most important criteria in forming portfolios. The present research aims at merging this criterion with Markowitz’s suggested model in Iran’s market using liquidity filtering, liquidity constraints and thus forming a model by using of which investors form a portfolio whose return, risk and liquidity is optimal. The research results show that liquidity in high levels has an effect on investors decisions and their efficient frontiers. 

The most important issue with trajectory analysis is calculating similarity between trajectories. In this paper a novel method for measuring similarity between trajectories based on the cost to match a set of trajectories segments was introduced. The similarity between two trajectories is defined as a minimum cost to match a trajectory to the other one. For this purpose, the segment based distance was introduced to as a cost of matching two trajectories segments. In addition, the dynamic programming technique is used to implement the time warp method. We performed some experiments to compare the proposed similarity measure with the similar approaches in the application of trajectory classification. The empirical quality of the proposed similarity measure was evaluated on 1-nearest neighbor (1-NN) classification task using 13 publicly available data sets. Compared to the other well-known similarity measures, the proposed method proved to be effective in the considered experiments based on the accuracy of classification.

Soil water retention curve is a key function that expresses soil vadose zone characteristics quantitatively. The direct measurement of this curve is time-consuming, laborious and costly. Therefore, many attempts have been made to predict water retention curve from other soil characteristics indirectly. Pedotransfer functions (PTFs) is one of the indirect methods. The objective of this research was to study the effect of geometric mean diameter (dg) and geometric standard deviation (σg) calculated the basis of three and nine soil particle size classes in the prediction of soil water retention curve and Van Genuchten equations parameters applying pedotransfer functions. Consequently, 40 loamy soil samples, including 35 samples for prediction and 5 samples for validation, were randomly collected from Karaj area. Particle size distribution, bulk density, calcium carbonate and organic carbon percentages were determined with the hydrometery, cold, acid neutralization and Wally and Blacks methods, respectively. Soil water retention curve was obtained using pressure plates. The best subset of independent variables for estimation of soil water retention curve and Van Genuchten equations parameters were selected by best subset regression command. Regression equations were obtained using multiple linear regressions. The results indicate that there is no significant difference in calculations in predicting point estimation PTFs by using dg or σg obtained from the data of three soil particle size classes or nine soil particle size classes. However, in the case of parametric estimation of water retention at tensions of 10, 33, and 100 kPa, using dg and σg obtained from the data of nine soil particle size classes and at tensions of 300, 500, 1500kPa than using dg and σg obtained from the data based on three soil particle size classes made more valid predictions. Statistical analysis indicated high validity of derived PTFs.

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