• School Mathematics
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• v.12 no.3
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• pp.273-299
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• 2010

The purpose of the study is designing and implementing 'Sampling Distributions Simulation' to help students to understand concepts of sampling distributions. This computer simulation is developed to help students understand sampling distributions more easily. 'Sampling Distributions Simulation' consists of 4 sessions. 'The first session - Confidence level and confidence intervals - includes checking if the intended confidence level is actually achieved by the real relative frequency for the obtained sample confidence intervals containing population mean. This will give the students clearer idea about confidence level and confidence intervals in addition to the role of sampling distribution of the sample means among those. 'The second session - Sampling Distributions - helps understand sampling distribution of the sample means, through the simulation method to make comparison between the histogram of sampling distributions and that of the population. The third session - The Central Limit Theorem - includes calculating the means of the samples taken from a population which follows a uniform distribution or follows a Bernoulli distribution and then making the histograms of those means. This will provides comprehension of the central limit theorem, which mentions about the sampling distribution of the sample means when the sample size is very large. The forth session - the normal approximation to the binomial distribution - helps understand the normal approximation to the binomial distribution as an alternative version of central limit theorem. With the practical usage of the shareware 'Sampling Distributions Simulation', we expect students to have a new vision on the sampling distribution and to get more emphasis on it. With the sound understandings on the sampling distributions, more accurate and profound statistical inferences are expected. And the role of the sampling distribution in the inferences should be more deeply appreciated.

• Honam Mathematical Journal
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• v.38 no.3
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• pp.613-623
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• 2016

As a generalization of the Fourier transform, the fractional Fourier transform plays an important role both in theory and in applications of signal processing. We present a new approach to reach a uniform sampling theorem in the shift-invariant spaces associated with the fractional Fourier transform domain.

• Journal of the Korean Statistical Society
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• v.36 no.2
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• pp.229-235
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• 2007

We consider a ruin model whose surplus process is formed by a compound Poisson process. If the level of surplus reaches V > 0, it is assumed that a certain amount of surplus is invested. In this paper, we apply the optional sampling theorem to the surplus process and obtain the expectation of period T, time from origin to the point where the level of surplus reaches either 0 or V. We also derive the total and average amount of surplus during T by establishing a backward differential equation.

• Communications for Statistical Applications and Methods
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• v.23 no.5
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• pp.423-432
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• 2016

In this paper, we stochastically analyze the continuous time surplus process in a risk model which involves a continuous type investment. It is assumed that the investment of the surplus to other business is continuously made at a constant rate, while the surplus process stays over a given sufficient level. We obtain the stationary distribution of the surplus level and/or its moment generating function by forming martingales from the surplus process and applying the optional sampling theorem to the martingales and/or by establishing and solving an integro-differential equation for the distribution function of the surplus level.

• Communications of the Korean Mathematical Society
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• v.14 no.3
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• pp.627-633
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• 1999

Let the given distribution $\pi$ have a log-concave density which is proportional to exp(-V(x)) on $R^d$. We consider a Markov chain induced by the method Gibbs sampling having $\pi$ as its in-variant distribution and prove geometric ergodicity and the functional central limit theorem for the process.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.257-269
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• 2001

The simulation is used to estimate an overflow probability in a stable parallel network with coupled inputs. Since the general simulation needs extremely many trials to obtain such a small probability, the fast simulation is proposed to reduce trials instead. By using the Cramer’s theorem, we first obtain an optimally changed measure under which the variance of the estimator is minimized. Then, we use it to derive an importance sampling estimator of the overflow probability which enables us to perform the fast simulation.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.969-990
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• 2016

We derive a sampling theorem associated with first order self-adjoint eigenvalue problem with a finite rank perturbation. The class of the sampled integral transforms is of finite Fourier type where the kernel has an additional perturbation.

• Communications for Statistical Applications and Methods
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• v.22 no.3
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• pp.295-304
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• 2015

This paper considers the problem of estimation of the Hurst parameter H ${\in}$ (1/2, 1) from longitudinal data with the error term of a fractional Brownian motion with Hurst parameter H that gives the amount of the long memory of its increment. We provide a new estimator of Hurst parameter H using a two scale sampling method based on $A{\ddot{i}}t$-Sahalia and Jacod (2009). Asymptotic behaviors (consistent and central limit theorem) of the proposed estimator will be investigated. For the proof of a central limit theorem, we use recent results on necessary and sufficient conditions for multi-dimensional vectors of multiple stochastic integrals to converges in distribution to multivariate normal distribution studied by Nourdin et al. (2010), Nualart and Ortiz-Latorre (2008), and Peccati and Tudor (2005).

• Journal of the Korean Institute of Telematics and Electronics
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• v.18 no.2
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• pp.22-26
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• 1981

Truncated expansions based upon the sampling theorem but containing only a few terms can be very useful for practical interpolations of band-limited or narrow-band random signals. The major goal of this work is to find and coiupare efficient and "statistically accurate" algorithms for the dynamic analysis of the ocean systems. The stalistical accuracy of truncated sampling interpolations is investicated, and one simple ocean systems, which yields a Runge-Kutta simulation algorithm of improved accuracy with very little increase in computation, is indicated.indicated.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.465-480
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• 2019

In the present article, we analyse the behaviour of a new family of Kantorovich type sampling operators $(K^{\varphi}_wf)_{w>0}$. First, we give a Voronovskaya type theorem for these Kantorovich generalized sampling series and a corresponding quantitative version in terms of the first order of modulus of continuity. Further, we study the order of approximation in $C({\mathbb{R}})$, the set of all uniformly continuous and bounded functions on ${\mathbb{R}}$ for the family $(K^{\varphi}_wf)_{w>0}$. Finally, we give some examples of kernels such as B-spline kernels and the Blackman-Harris kernel to which the theory can be applied.