A statistical distribution of quad-pol X-band sea clutter time series acquired at a grazing angle

Although the complex Wishart distribution has been widely used to analyze the statistic properties of quad-pol SAR spatial data, the applicability of this complex distribution to the time series of sea clutter is rarely discussed.The measured data of the quad-pol X-band marine radar demonstrate that the time series of the sea echoes are also satisfied the circular Gaussian distributions if the low intensity signals, which are mainly dominated by a radar noise, in the shadow regions of the large-scale waves are removed. On the basis of this fact, the probability density functions（PDFs） of the intensity as well as the phase, the real and the imaginary parts of the sea echoes obtained by the marine radar have been derived, and the theoretical models are all expressed in closed forms. In order to validate the theoretical results, the PDFs are compared with the experimental data collected by the Mc Master IPIX radar. And the comparisons show that the PDF models are in good agreement with the experimental data.

Numerical Prediction of Statistical Masonry Wall Fragment Distribution Induced by Blast Loading

The hazard caused by the fragments of damaged structures is usually significant in acci-dental explosions or hostile blast events.A reliable and efficient method to estimate probable fragment size,velocity and launch distance will be useful to assess and design countermeasures to mitigate the possible fragment hazards.This paper presents a numerical method for predicting the size and launch distance of the fragments caused by explosive damage of masonry wall.Numerical simulations with different scaled distances are carried out,and the statistical distribution functions of the fragment size and launch distance in terms of the scaled distance are derived.

Appropriateness of Reduced Modified Three-Parameter Weibull Distribution Function for Predicting Gold Production in Ghana

Forecasting mine production is pertinent to gold mining as it serves as production goals for investors. It is therefore important to identify the exact distribution that gold production as a response variable naturally follows. It is even more appropriate to have a model(s) with few predictor variables. This paper seeks to identify appropriate statistical distribution functions for fitting gold production in Ghana. The empirical paper relied mainly on quarterly secondary datasets on gold production between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Weibull, Log-Normal, Generalized Extreme Value (GEV) were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC, AICc and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the reduced modified 3-parameter Weibull distribution provided the best fit for gold production in Ghana. Though the reduced modified Weibull function is proposed, it is important however to recognize that other external factors can influence production levels. Also, the average quarterly fitted gold production is 1000334.8918 ± 75,327.080 (±7.5%) [i.e., 925,007.812 – 1,075,661.972]. This indicates that the average annually fitted gold production lies between 3700031.248 and 4302647.888 ounces at 99.9% confidence level. Therefore, the predicted gold production for the year 2022 is 3.7million ounces at 99.9% confidence level.

Appropriateness of Reduced Modified Three-Parameter Weibull Distribution Function for Predicting Gold Production in Ghana

Forecasting mine production is pertinent to gold mining as it serves as production goals for investors. It is therefore important to identify the exact distribution that gold production as a response variable naturally follows. It is even more appropriate to have a model(s) with few predictor variables. This paper seeks to identify appropriate statistical distribution functions for fitting gold production in Ghana. The empirical paper relied mainly on quarterly secondary datasets on gold production between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Weibull, Log-Normal, Generalized Extreme Value (GEV) were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC, AICc and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the reduced modified 3-parameter Weibull distribution provided the best fit for gold production in Ghana. Though the reduced modified Weibull function is proposed, it is important however to recognize that other external factors can influence production levels. Also, the average quarterly fitted gold production is 1000334.8918 ± 75,327.080 (±7.5%) [i.e., 925,007.812 – 1,075,661.972]. This indicates that the average annually fitted gold production lies between 3700031.248 and 4302647.888 ounces at 99.9% confidence level. Therefore, the predicted gold production for the year 2022 is 3.7million ounces at 99.9% confidence level.

Nonequilibrium Statistical Nature of Intergranular Brittle Fracture in Polycrystal

The brittle fracture probability and reliability are obtained in terms of dislocation mechanism of microcrack evolution. The statistical distribution functions and statistical deviations of elongation, strength, plastic work, crack extension force, fracture foughness, critical and crack length, can be derived in a unified fashion.

Wave Energy Estimation by Using A Statistical Analysis and Wave Buoy Data near the Southern Caspian Sea

Statistical analysis was done on simultaneous wave and wind using data recorded by discus-shape wave buoy. The area is located in the southern Caspian Sea near the Anzali Port. Recorded wave data were obtained through directional spectrum wave analysis. Recorded wind direction and wind speed were obtained through the related time series as well. For 12-month measurements（May 25 2007-2008）, statistical calculations were done to specify the value of nonlinear auto-correlation of wave and wind using the probability distribution function of wave characteristics and statistical analysis in various time periods. The paper also presents and analyzes the amount of wave energy for the area mentioned on the basis of available database. Analyses showed a suitable comparison between the amounts of wave energy in different seasons. As a result, the best period for the largest amount of wave energy was known. Results showed that in the research period, the mean wave and wind auto correlation were about three hours. Among the probability distribution functions, i.e Weibull, Normal, Lognormal and Rayleigh, ＂Weibull＂ had the best consistency with experimental distribution function shown in different diagrams for each season. Results also showed that the mean wave energy in the research period was about 49.88 k W/m and the maximum density of wave energy was found in February and March, 2010.

THE RAMANUJAN'S Q-EXTENSION FOR THE EXPONENTIAL FUNCTION AND STATISTICAL DISTRIBUTIONS

In this paper. we shall propose a q-extension for the exponential function and develop q-analogs for families of statistical distribution, such as,the normal, and Poisson distribution etc.Many properties of these families will be studied.

Estimation of maximum inclusion by statistics of extreme values method in bearing steel

A statistic method, statistics of extreme values （SEV）, was described in detail, which can esti mate the size of maximum inclusion in steel. The characteristic size of the maximum inclusion in a high clean bearing steel （GCrl5） was evaluated by this method, and the morphology and corn position of large inclusions found were analyzed by scanning electron microscopy （SEM）. When standard inspection area （S0） is 280 mm2, the characteristic size of the biggest inclusion found in 30 standard inspection area is 23.93 μm, and it has a 99.9% probability of the characteristic size of maximum inclusion predicted being no larger than 36.85μm in the experimental steel. SEM result shows that large inclusions found are mainly composed of CaS, calcium-aluminate and MgO. Compositing widely exists in large inclusions in high clean bearing steel. Compared with traditional evaluation method, SEV method mainly focuses on inclusion size, and the esti- mation result is not affected by inclusion types. SEV method is suitable for the inclusion eval uation of high clean bearing steel.