Frequency Domain Goodness of Fit Test Based Spectrum Sensing Method with Dynamically Varying Noise

In cognitive radio networks,spectrum sensing under circumstances of dynamically varying noise and lacking prior information is a key challenge to the conventional spectrum sensing algorithms.Since the necessary information is rather difficult to obtain practically,most existing spectrum sensing methods are fettered in applications.Motivated by these,in this paper,a Frequency domain Goodness of Fit Test(FGoF)based spectrum sensing method is proposed.The FGoF makes full use of underlying information in Guard-Bands and the advantages of GoF test works for any distribution.Analytical and simulated results show that the FGoF is a robust spectrum sensing method in cognitive radio with the inherent advantages of invulnerability to dynamically varying noise.

Nonlinear Fitting Method of Long-Term Distributions for Statistical Analysis of Extreme Negative Surge Elevations

Hydrologic frequency analysis plays an important role in coastal and ocean engineering for structural design and disaster prevention in coastal areas. This paper proposes a Nonlinear Least Squares Method (NLSM), which estimates the three unknown parameters of the Weibull distribution simultaneously by an iteration method. Statistical test shows that the NLSM fits each data sample well. The effects of different parameter-fitting methods, distribution models, and threshold values are also discussed in the statistical analysis of storm set-down elevation. The best-fitting probability distribution is given and the corresponding return values are estimated for engineering design.

Comparative study of probable maximum precipitation and isohyetal maps for mountainous regions, Pakistan

Probable maximum precipitation(PMP) is widely used by hydrologists for appraisal of probable maximum flood(PMF)used for soil and water conservation structures, and design of dam spillways. A number of methods such as empirical, statistical and dynamic are used to estimate PMP, the most favored being statistical and hydro-meteorological. In this paper,PMP estimation in mountainous regions of Pakistan is studied using statistical as well as physically based hydro-meteorological approaches. Daily precipitation, dew point, wind speed and temperature data is processed to estimate PMP for a one-day duration. Maximum precipitation for different return periods is estimated by using statistical approaches such as Gumble and Log-Pearson type-III(LP-III) distribution. Goodness of fit(GOF) test, chi-square test, correlation coefficient and coefficient of determination were applied to Gumble and LP-III distributions. Results reveal that among statistical approaches, Gumble distribution performed the best result compared to LP-III distribution. Isohyetal maps of the study area at different return periods are produced by using the GIS tool, and PMP in mountainous regions varies from 150 to 320 mm at an average value of 230.83 mm. The ratio of PMP for one-day duration to highest observed rainfall(HOR) varied from 1.08 to 1.29 with an average value of 1.18. An appropriate frequency factor(K_m) is very important which is a function of mean for observed precipitation and PMP for 1-day duration, and K_m values varies from 2.54 to 4.68. The coefficient of variability(C_v) varies from minimum value of 28% to maximum value of 43.35%. It was concluded that the statistical approach gives higher results compared to moisture maximization(MM) approach. In the hydro-meteorological approach, moisture maximization(MM) and wind moisture maximization(WMM) techniques were applied and it was concluded that wind moisture maximization approach gives higher results of PMP as compared to moisture maximization approach as well as for Hershfield technique. Therefore, it is suggested that MM approach is the most favored in the study area for PMP estimation, which leads to acceptable results, compared to WMM and statistical approaches.

Consistency of Chi-Squared Test with Varying Number of Classes

The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of classes varying with sample size in the test has attached more and more attention.However,in this situation,there is not theoretical results for the asymptotic property of such chi-squared test statistic.This paper proves the consistency of chi-squared test with varying number of classes under some conditions.Meanwhile,the authors also give a convergence rate of KolmogorovSimirnov distance between the test statistic and corresponding chi-square distributed random variable.In addition,a real example and simulation results validate the reasonability of theoretical result and the superiority of chi-squared test with varying number of classes.

Inverse Length Biased Maxwell Distribution:Statistical Inference with an Application

In this paper,we suggested and studied the inverse length biased Maxell distribution(ILBMD)as a new continuous distribution of one parameter.The ILBMD is obtained by considering the inverse transformation technique of the Maxwell length biased distribution.Statistical characteristics of the ILBMD such as the moments,moment generating function,mode,quantile function,the coefficient of variation,coefficient of skewness,Moors and Bowley measures of kurtosis and skewness,stochastic ordering,stress-strength reliability,and mean deviations are obtained.In addition,the Bonferroni and Lorenz curves,Gini index,the reliability function,the hazard rate function,the reverse hazard rate function,the odds function,and the distributions of order statistics for the ILBMD,are presented.The ILBMD parameter is estimated using the maximum likelihood method,the method of moments,the maximum product of spacing technique,the ordinary and weight least square procedures,and the Cramer-Von-Mises methods.The Fishers information,as well as the Rényi and q-entropies,are derived.To investigate the usefulness of the proposed lifetime distribution and to illustrate the purpose of the study,a real dataset of the relief times of 20 patients receiving an analgesic is used.

Blind spectrum sensing based on the ratio of mean square to variance

Anderson-Darling （AD） sensing, characteristic function （CF） sensing and order statistic （OS） sensing are three common spectrum sensing （SS） methods based on goodness of fit （GOF） testing. However, AD and OS sensing needs the prior information of noise variance; CF and OS sensing have high computation complexity. To circumvent those difficulties, in this paper, the ratio of the mean square to variance （RM2V） of the samples, after deriving its probability density function （PDF）, is employed as a test statistic to detect the availability of the vacant spectrum in the cognitive radio （CR） system. Then a blind SS method based on RM2V is proposed, which is dubbed as RM2V sensing, and its exact theoretical threshold is obtained via the derived PDF of RM2V. The performance of RM2V sensing is evaluated by theoretical analysis and Monte Carlo simulations. Comparing with the conventional energy detection （ED）, AD, CF and OS sensing, RM2V sensing, with no need of noise variance, has advantages from the aspect of computation complexity and detection performance.