Test of Generating Function and Estimation of Equivalent Radius in Some Weapon Systems and Its Stochastic Simulation

Author(s)
Famei Zheng

ABSTRACT

We discuss three-dimensional uniform distribution and its property in a sphere; give a method of assessing the tactical and technical indices of cartridge ejection uniformity in some type of weapon systems. Meanwhile we obtain the test of generating function and the estimation of equivalent radius. The uniformity of distribution is tested and verified with ω2 test method on the basis of stochastic simulation example.

We discuss three-dimensional uniform distribution and its property in a sphere; give a method of assessing the tactical and technical indices of cartridge ejection uniformity in some type of weapon systems. Meanwhile we obtain the test of generating function and the estimation of equivalent radius. The uniformity of distribution is tested and verified with ω2 test method on the basis of stochastic simulation example.

KEYWORDS

Uniform Distribution in a Sphere, Weapon Systems, Generating Function, Equivalent Radius, Stochastic Simulation

Uniform Distribution in a Sphere, Weapon Systems, Generating Function, Equivalent Radius, Stochastic Simulation

Cite this paper

nullF. Zheng, "Test of Generating Function and Estimation of Equivalent Radius in Some Weapon Systems and Its Stochastic Simulation,"*Applied Mathematics*, Vol. 2 No. 12, 2011, pp. 1546-1550. doi: 10.4236/am.2011.212220.

nullF. Zheng, "Test of Generating Function and Estimation of Equivalent Radius in Some Weapon Systems and Its Stochastic Simulation,"

References

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[7] F. M. Zheng, “Estimate of Radius on Three-Dimensional Uniform Distribution in a Sphere,” Mathematics in Practice and Theory, Vol. 40, No. 14, 2010, pp. 166-170.

[8] Y. X. Liu and P. Cheng, “Uniform Distribution of Ball PPCM Test Statistic on Dimension and Sample Size Berry-Esseen Boundary and LIL,” China Science Bulletin, Vol. 43, No. 13, 2005, pp. 1452-1453.

[9] S. R. Xie, “Two Types of Stay Limit Theorems of Non-Stationary Gaussian Process,” Science in China, Series A, Vol. 23, No. 4, 1993, pp. 369-376.

[10] Z. S. Hu and C. Su, “Limit Theorems for the Number and Sum of Near-Maxima for Medium Tails,” Statistics & Probability Letters, Vol. 63, No. 3, 2003, pp. 229-237. doi:10.1016/S0167-7152(03)00085-3

[11] Y. Qi, “Limit Distributions for Products of Sums,” Statistics & Probability Letters, Vol. 62, No. 1, 2007, pp. 93-100. doi:10.1016/S0167-7152(02)00438-8

[12] G. Rempala and J. Wesolowski, “Asymptotics for Products of Sums and U-Statistics,” Electronic Communications in Probability, Vol. 7, No. 7, 2002, pp. 47-54.

[13] K. T. Fang, J. Q. Fan, H. Jin, et al., “Statistical Analysis of Directional Date,” Journal of Application of Statistics and Management, Vol. 9, No. 2, 1990, pp. 59-65.

[14] M. D. Troutt, W. K. Pang and S. H. Hou, “Vertical Density Representation and Its Applications,” World Scientific Publishing Co. Pte. Ltd, Singapore, 2004. doi:10.1142/9789812562616

[15] Z. S. Wei, “Probability Theory and Mathematical Statistics,” Higher Education Press, Beijing, 1983.

[16] S. M. Berman, “Extreme Sojourns of a Gaussian Process with a Point of Maximum Variance,” Probability Theory and Related Fields, Vol. 74, 1987, pp. 113-124. doi:10.1007/BF01845642

[17] C. P. Pan and Z. J. Han, “Probability and Statistic of Weapon Test,” National Defence Industry Press, Beijing, 1979.

[18] N. I. Sidnyaev and K. S. Andreytseva, “Independence of the Residual Quadratic Sums in the Dispersion Equation with Noncentral χ2-Distribution,” Applied Mathematics, Vol. 2, No. 2, 2011, pp. 1303-1308.

[1] G. S. Chen, “Interval Estimate of the Interval Length on Uniform Distribution,” Pure and Applied Mathematics, Vol. 22, No. 3, 2006, pp. 349-354.

[2] H. B. Zhang, “The Shortest Confidence Interval of the Interval Length on Uniform Distribution,” Journal of Xiaogan University, Vol. 27, No. 3, 2007, pp. 52-55.

[3] Z. J. Liu, “Estimate of Rectangle Region Area on Two Dimensional Uniform Distribution,” College Mathematics, Vol. 23, No. 4, 2007, pp. 155-159.

[4] Z. J. Liu, “Estimate of Cuboid Volume on Three-Dimensional Uniform Distribution,” Statistics and Decision, No. 5, 2007, pp. 23-24.

[5] Z. X. Wang, “Parameter Estimation of Two-Dimensional Uniform Distribution in a Circle,” College Mathematics, Vol. 24, No. 2, 2008, pp. 150-152.

[6] W. Q. Jin, D. S. Cui and B. Deng, “On the Testing and Estimation of Uniform Distribution in a Circle,” Acta Armamentarii, Vol. 22, No. 4, 2001, pp. 468-472.

[7] F. M. Zheng, “Estimate of Radius on Three-Dimensional Uniform Distribution in a Sphere,” Mathematics in Practice and Theory, Vol. 40, No. 14, 2010, pp. 166-170.

[8] Y. X. Liu and P. Cheng, “Uniform Distribution of Ball PPCM Test Statistic on Dimension and Sample Size Berry-Esseen Boundary and LIL,” China Science Bulletin, Vol. 43, No. 13, 2005, pp. 1452-1453.

[9] S. R. Xie, “Two Types of Stay Limit Theorems of Non-Stationary Gaussian Process,” Science in China, Series A, Vol. 23, No. 4, 1993, pp. 369-376.

[10] Z. S. Hu and C. Su, “Limit Theorems for the Number and Sum of Near-Maxima for Medium Tails,” Statistics & Probability Letters, Vol. 63, No. 3, 2003, pp. 229-237. doi:10.1016/S0167-7152(03)00085-3

[11] Y. Qi, “Limit Distributions for Products of Sums,” Statistics & Probability Letters, Vol. 62, No. 1, 2007, pp. 93-100. doi:10.1016/S0167-7152(02)00438-8

[12] G. Rempala and J. Wesolowski, “Asymptotics for Products of Sums and U-Statistics,” Electronic Communications in Probability, Vol. 7, No. 7, 2002, pp. 47-54.

[13] K. T. Fang, J. Q. Fan, H. Jin, et al., “Statistical Analysis of Directional Date,” Journal of Application of Statistics and Management, Vol. 9, No. 2, 1990, pp. 59-65.

[14] M. D. Troutt, W. K. Pang and S. H. Hou, “Vertical Density Representation and Its Applications,” World Scientific Publishing Co. Pte. Ltd, Singapore, 2004. doi:10.1142/9789812562616

[15] Z. S. Wei, “Probability Theory and Mathematical Statistics,” Higher Education Press, Beijing, 1983.

[16] S. M. Berman, “Extreme Sojourns of a Gaussian Process with a Point of Maximum Variance,” Probability Theory and Related Fields, Vol. 74, 1987, pp. 113-124. doi:10.1007/BF01845642

[17] C. P. Pan and Z. J. Han, “Probability and Statistic of Weapon Test,” National Defence Industry Press, Beijing, 1979.

[18] N. I. Sidnyaev and K. S. Andreytseva, “Independence of the Residual Quadratic Sums in the Dispersion Equation with Noncentral χ2-Distribution,” Applied Mathematics, Vol. 2, No. 2, 2011, pp. 1303-1308.