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A simulation-based Bayesian study is used for assessing if the threshold parameter can be taken to be zero or positive in situations representing the two Weibull distribution models. The compatibility of the models for the given data set is studied and Gibbs sampling is used for conducting the posterior simulation in each case.

Full Bayes analysis is proposed for the Pareto distribution with doubly-censored observations while a Gibbs sampler algorithm is used for generating sample-based estimated of posterior distributions. The computationally simple approach accurately analyzed the low-dimensional posterior surfaces. Censored data complexities, which normally arise in non sample-based methods, were effectively addressed by the Gibbs sampler algorithm.

The continuous wavelet transform of Schwartz tempered distributions is investigated and derive the corresponding wavelet inversion formula (valid modulo a constant-tempered distribution) interpreting convergence in S ′ (R). But uniqueness theorem for the present wavelet inversion formula is valid for the space S F ′ (R) obtained by filtering (deleting) (i) all non-zero constant distributions from the space S ′ (R) , (ii) all non-zero constants that appear with a distribution as a union. As an example, in considering the distribution x 2 1 + x 2 = 1 − 1 1 + x 2 we would omit 1 and retain only − 1 1 + x 2 . The wavelet kernel under consideration for determining the wavelet transform are those wavelets whose all the moments are non-zero. As an example, (1 + k x − 2 x 2) e − x 2 is such a wavelet. k is an arbitrary constant. There exist many other classes of such wavelets. In our analysis, we do not use a wavelet kernel having any of its moments zero. [ABSTRACT FROM AUTHOR]

In this paper, Cauchy wavelet transform of ultra-distributions in tube domains is defined and its various properties are studied using the theory of Cauchy integrals and Poisson integrals of ultra-distributions. [ABSTRACT FROM PUBLISHER]

Exponential and Weibull models are commonly used models with former being the special case of the latter. In their most general forms, the exponential model involves both threshold and scale parameters whereas the Weibull model involves threshold, scale and shape parameters. The article analyzes the two models in a Bayesian framework and examines the feasibility of generality versus particularity in the sense that it tests for the possibility of (not) having a threshold and/or a shape parameter in the data arising from exponential (Weibull) model. The results are illustrated based on both complete and censored datasets from the models. [ABSTRACT FROM PUBLISHER]

The paper considers a lognormal model for the survival times and obtains a Bayes solution by means of Gibbs sampler algorithm when the priors for the parameters are vague. The formulation given in the paper is mainly focused for censored data problems though it is equally well applicable for complete data scenarios as well. For the purpose of numerical illustration, we considered two real data sets on head and neck cancer patients when they have been treated using either radiotherapy or chemotherapy followed by radiotherapy. The paper not only compares the survival functions for the two therapies assuming a lognormal model but also provides a model compatibility study based on predictive simulation results so that the choice of lognormal model can be justified for the two data sets. The ease of our analysis as compared to an earlier approach is certainly an advantage. [ABSTRACT FROM PUBLISHER]

Abstract: Motivated from Wong [M.W. Wong, -Boundedness of localization operators associated to left regular representations, Proc. Amer. Math. Soc. 130 (2002) 2911–2929], an -boundedness of localization operators associated to Bessel''s left regular representations of locally compact Hausdorff group is obtained and an application of Bessel wavelet multipliers is investigated by using Zemanian theory of Hankel transformation. [Copyright &y& Elsevier]

In this paper the Banach-space-valued generalized functions of ultradistributions of type ( H ω μ ( A ))′ is investigated and using the theory of Hankel transformation its properties are studied. [ABSTRACT FROM AUTHOR]

Discusses how an asymptotic series of general symbol of pseudo-differential operators associated with Bessel operators are obtained. Use of the Hankel convolution; Details on the procedure used.

Analyzes the parameter lognormal distribution using Gibbs sampler. Extension of the algorithm; Effect of censoring on the analysis of lognormal model; Description of the Gibbs sampler scheme.