The basic inference function of mathematical statistics, the score function, is a vector function. The author has introduced the scalar score, a scalar inference function, which reflects main features of a continuous ...The basic inference function of mathematical statistics, the score function, is a vector function. The author has introduced the scalar score, a scalar inference function, which reflects main features of a continuous probability distribution and which is simple. Its simplicity makes it possible to introduce new relevant numerical characteristics of continuous distributions. The t-mean and score variance are descriptions of distributions without the drawbacks of the mean and variance, which may not exist even in cases of regular distributions. Their sample counterparts appear to be alternative descriptions of the observed data. The scalar score itself appears to be a new mathematical tool, which could be used in solving traditional statistical problems for models far from the normal one, skewed and heavy-tailed.展开更多
For the stochastic structure with stochastic excitation, an advanced stratified line sampling (SLS) method is presented to obtain the cumulative distribution function (CDF) of the structural response and its sensitivi...For the stochastic structure with stochastic excitation, an advanced stratified line sampling (SLS) method is presented to obtain the cumulative distribution function (CDF) of the structural response and its sensitivity. The advanced stratified line sampling method introduces a set of middle failure subsets firstly. And for each subset, the conventional line sampling can be used to obtain the corresponding value of the response's CDF. At the same time, the sensitivity estimations of each failure subset can also be computed by modifying the important direction and corresponding reliability coefficients. The properties of CDF sensitivity are proved while the performance function is linear with normal random variables. After two simple examples are used to demonstrate the properties of CDF sensitivity and the feasibility of the presented method, the method employed to analyze the CDF and corresponding sensitivity of root bending moment (RBM) responses for the stochastic BAH is wing with gust excitation to a square-edged gust and to a Dryden gust. The results show that the parameters of the second and the fifth order modals exert more influence on the CDF of response than the other ones, and the presented SLS method can more significantly reduce the computational cost compared with Monte Carlo simulation (MCS).展开更多
In this paper we consider the problem of estimation of a continuous distribution function under the LINEX loss function. The best invariant estimator is obtained and proved to be minimax for any sample size n ≥ 1.
Stars are born in dense cores of molecular clouds. The core mass function （CMF）, which is the mass distribution of dense cores, is important for understanding the stellar initial mass function （IMF）. We obtained ...Stars are born in dense cores of molecular clouds. The core mass function （CMF）, which is the mass distribution of dense cores, is important for understanding the stellar initial mass function （IMF）. We obtained 350μm dust continuum data using the SHARC-II camera at the Caltech Submillimeter Observatory （CSO） telescope. A 350μm map covering 0.25 deg2 of the Ophiuchus molecular cloud was created by mosaicing 56 separate scans. The CSO telescope had an angular resolution of 9＂, corresponding to 1.2 ×103 AU at the distance of the Ophiuchus molecular cloud （131 pc）. The data was reduced using the Comprehensive Reduction Utility for SHARC-II （CRUSH）. The flux density map was analyzed using the GaussClumps algorithm, within which 75 cores has been identified. We used the Spitzer c2d catalogs to separate the cores into 63 starless cores and 12 protostellar cores. By locating Jeans instabilities, 55 prestellar cores （a subcategory of starless cores） were also identified. The excitation temperatures, which were derived from FCRAO 12CO data, help to improve the accuracy of the masses of the cores. We adopted a Monte Carlo approach to analyze the CMF with two types of functional forms; power law and log-normal. The whole and prestellar CMF are both well fitted by a log-normal distribution, with p = -1. 18 ±0.10, σ = 0.58 ± 0.05 and μ= 1.40 ＋ 0.10, σ= 0.50 ＋ 0.05 respectively. This finding suggests that turbulence influences the evolution of the Ophiuchus molecular cloud.展开更多
We assume T1,..., Tn are i.i.d. data sampled from distribution function F with density function f and C1,...,Cn are i.i.d. data sampled from distribution function G. Observed data consists of pairs （Xi, δi）, em= 1,...We assume T1,..., Tn are i.i.d. data sampled from distribution function F with density function f and C1,...,Cn are i.i.d. data sampled from distribution function G. Observed data consists of pairs （Xi, δi）, em= 1,..., n, where Xi = min{Ti,Ci}, δi = I（Ti 6 Ci）, I（A） denotes the indicator function of the set A. Based on the right censored data {Xi, δi}, em=1,..., n, we consider the problem of estimating the level set {f 〉 c} of an unknown one-dimensional density function f and study the asymptotic behavior of the plug-in level set estimators. Under some regularity conditions, we establish the asymptotic normality and the exact convergence rate of the λg-measure of the symmetric difference between the level set {f ≥ c} and its plug-in estimator {fn ≥ c}, where f is the density function of F, and fn is a kernel-type density estimator of f. Simulation studies demonstrate that the proposed method is feasible. Illustration with a real data example is also provided.展开更多
文摘The basic inference function of mathematical statistics, the score function, is a vector function. The author has introduced the scalar score, a scalar inference function, which reflects main features of a continuous probability distribution and which is simple. Its simplicity makes it possible to introduce new relevant numerical characteristics of continuous distributions. The t-mean and score variance are descriptions of distributions without the drawbacks of the mean and variance, which may not exist even in cases of regular distributions. Their sample counterparts appear to be alternative descriptions of the observed data. The scalar score itself appears to be a new mathematical tool, which could be used in solving traditional statistical problems for models far from the normal one, skewed and heavy-tailed.
基金the National Nature Science Foundation of China (Grant No. 51175425)the Aviation Science Foundation (Grant No. 2011ZA53015)+1 种基金the Aerospace Science and Technology Innovative Foundation (Grant No. 2011200093)the Nature Science Basic Research Fund of Shaanxi Province (Grant No. 2012JQ1015)
文摘For the stochastic structure with stochastic excitation, an advanced stratified line sampling (SLS) method is presented to obtain the cumulative distribution function (CDF) of the structural response and its sensitivity. The advanced stratified line sampling method introduces a set of middle failure subsets firstly. And for each subset, the conventional line sampling can be used to obtain the corresponding value of the response's CDF. At the same time, the sensitivity estimations of each failure subset can also be computed by modifying the important direction and corresponding reliability coefficients. The properties of CDF sensitivity are proved while the performance function is linear with normal random variables. After two simple examples are used to demonstrate the properties of CDF sensitivity and the feasibility of the presented method, the method employed to analyze the CDF and corresponding sensitivity of root bending moment (RBM) responses for the stochastic BAH is wing with gust excitation to a square-edged gust and to a Dryden gust. The results show that the parameters of the second and the fifth order modals exert more influence on the CDF of response than the other ones, and the presented SLS method can more significantly reduce the computational cost compared with Monte Carlo simulation (MCS).
基金This research is supported by National Natural Science Foundation of China （No. 10571070）.
文摘In this paper we consider the problem of estimation of a continuous distribution function under the LINEX loss function. The best invariant estimator is obtained and proved to be minimax for any sample size n ≥ 1.
基金by the California Institute of Technology under cooperative agreement with the National Science Foundation (Grant No. AST0838261)supported by National Basic Research Program of China (Grant No. 2012CB821800)+2 种基金National Aeronautics and Space Administration Undergraduate Student Research Program of USANational Natural Science Foundation of China (Grant Nos. 11373038 and 11163002)Graduate Innovative Fund of Gui Zhou University (Grant Nos. 2013024)
文摘Stars are born in dense cores of molecular clouds. The core mass function （CMF）, which is the mass distribution of dense cores, is important for understanding the stellar initial mass function （IMF）. We obtained 350μm dust continuum data using the SHARC-II camera at the Caltech Submillimeter Observatory （CSO） telescope. A 350μm map covering 0.25 deg2 of the Ophiuchus molecular cloud was created by mosaicing 56 separate scans. The CSO telescope had an angular resolution of 9＂, corresponding to 1.2 ×103 AU at the distance of the Ophiuchus molecular cloud （131 pc）. The data was reduced using the Comprehensive Reduction Utility for SHARC-II （CRUSH）. The flux density map was analyzed using the GaussClumps algorithm, within which 75 cores has been identified. We used the Spitzer c2d catalogs to separate the cores into 63 starless cores and 12 protostellar cores. By locating Jeans instabilities, 55 prestellar cores （a subcategory of starless cores） were also identified. The excitation temperatures, which were derived from FCRAO 12CO data, help to improve the accuracy of the masses of the cores. We adopted a Monte Carlo approach to analyze the CMF with two types of functional forms; power law and log-normal. The whole and prestellar CMF are both well fitted by a log-normal distribution, with p = -1. 18 ±0.10, σ = 0.58 ± 0.05 and μ= 1.40 ＋ 0.10, σ= 0.50 ＋ 0.05 respectively. This finding suggests that turbulence influences the evolution of the Ophiuchus molecular cloud.
基金supposed by National Natural Science Foundation of China (Grant Nos. 11071137 and 11371215)Tsinghua Yue-Yuen Medical Science Fund
文摘We assume T1,..., Tn are i.i.d. data sampled from distribution function F with density function f and C1,...,Cn are i.i.d. data sampled from distribution function G. Observed data consists of pairs （Xi, δi）, em= 1,..., n, where Xi = min{Ti,Ci}, δi = I（Ti 6 Ci）, I（A） denotes the indicator function of the set A. Based on the right censored data {Xi, δi}, em=1,..., n, we consider the problem of estimating the level set {f 〉 c} of an unknown one-dimensional density function f and study the asymptotic behavior of the plug-in level set estimators. Under some regularity conditions, we establish the asymptotic normality and the exact convergence rate of the λg-measure of the symmetric difference between the level set {f ≥ c} and its plug-in estimator {fn ≥ c}, where f is the density function of F, and fn is a kernel-type density estimator of f. Simulation studies demonstrate that the proposed method is feasible. Illustration with a real data example is also provided.
