• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.253-260
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• 2001

In this paper we suggest a conditional unrelated question randomized response model by using the Carr et. al.’s model(1982) and Greenberg et. al.’s model(1969). Our model can obtain more comprehensive information about the sensitive character A. We suggest the conditions that make our model efficient compared with models of Greenberg et. al. and Carr et al..

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.721-729
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• 2000

In this paper, we propose a new conditional randomized response model that has improved the Carr et al.'s model in view of he variance and the protection of privacy of respondents. We show that he suggested model is more effective and protective than the Loynes' model and Carr et al.' model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.4
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• pp.249-273
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• 2010

Often in practice, the implied volatility of an option is calculated to find the option price tomorrow or the prices of, nearby' options. To show that one does not need to adhere to the Black- Scholes formula in this scheme, Figlewski has provided a new pricing formula and has shown that his, alternating passive model' performs as well as the Black-Scholes formula [8]. The Figlewski model was modified by Henderson et al. so that the formula would have no static arbitrage [10]. In this paper, we show how to construct a huge class of such static no arbitrage pricing functions, making use of distortions, coherent risk measures and the pricing theory in incomplete markets by Carr et al. [4]. Through this construction, we provide a more elaborate static no arbitrage pricing formula than Black-Sholes in the above scheme. Moreover, using our pricing formula, we find a volatility curve which fits with striking accuracy the synthetic data used by Henderson et al. [10].

• Journal of the Korean Data Analysis Society
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• v.20 no.6
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• pp.2883-2893
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• 2018

We suggest a stratified conditional unrelated question randomized response model to more efficiently estimate a sensitive character A when the population is composed of several strata. In that model, only the respondents who answered "yes" through randomization device which was consisted of a less sensitive character B and a question forcing to answer "yes" respond to our suggested model and we deal with two allocation problems of proportional allocation and optimal one. We expand the suggested model into two sample stratified conditional unrelated question model to cover the case of unknowing unrelated character and deduce minimal variance through optimal sample size of stratum h. Finally, we show that the suggested model is more efficiency than stratified unrelated models and the stratified Carr et al.'s model (1982) under some given conditions, and show numerically that the smaller the values ${\pi}_{h2}$ and ${\pi}_{hy}$, the more efficiency the fit of the model.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.825-835
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• 2002

In this paper, we extend the conditional unrelated question model which was suggested by Lee and Hong(2000) to two-sample case when there is no information about the true proportion of the unrelated character Y. Conditions are obtained under which the proposed model is more efficient than Carr et al.\`s conditional modal and Greenberg et al.'s two-sample unrelated question model.