Background & Aim: In the survival data with Long-term survivors the event has not occurred for all the patients despite long-term follow-up, so the survival time for a certain percent is censored at the end of the study. Mixture cure model was introduced by Boag, 1949 for reaching a more efficient analysis of this set of data. Because of some disadvantages of this model non-mixture cure model was introduced by Chen, 1999, which became well-known promotion time cure model. This model was based on the latent variable distribution of N. Non mixture cure models has obtained much attention after the introduction of the latent activating Scheme of Cooner, 2007, in recent decades, and diverse distributions have been introduced for latent variable.Methods & Materials: In this article, generalized Poisson-inverse Gaussian distribution (GPIG) will be presented for the latent variable of N, and the novel model which is obtained will be utilized in analyzing long-term survival data caused by skin cancer. To estimate the model parameters with Bayesian approach, numerical methods of Monte Carlo Markov chain will be applied. The comparison drawn between the models is on the basis of deviance information criteria (DIC). The model with the least DIC will be selected as the best model.Results: The introduced model with GPIG, with deviation criterion of 411.775, had best fitness than Poisson and Poisson-inverse Gaussian distribution with deviation criterion of 426.243 and 414.673, respectively.Conclusion: In the analyzing long-term survivors, to overcome high skewness and over dispersion using distributions that consist of parameters to estimate these statistics may improve the fitness of model. Using distributions which are converted to simpler distributions in special occasions, can be applied as a criterion for comparing other models.

Recently, Alizadeh and Shafaei (2023) introduced some estimators for varentropy of a continuous random variable. The present article applies these estimators and construct some tests of fit for Inverse Gaussian distribution. Percentage points and type I error of the new tests are obtained and then power values of the proposed tests against various alternatives are computed. The results of a simulation study show that the tests have a good performance in terms of power. Finally, a real data set is used to illustrate the application of the proposed tests.

The Inverse Gaussian (IG) distribution is widely used to model positively skewed data. In this article, we examine goodness of fit tests for the Inverse Gaussian distribution based on the empirical distribution function. In order to compute the test statistics, parameters of the Inverse Gaussian distribution are estimated by maximum likelihood estimators (MLEs), which are simple explicit estimators. Critical points and the actual sizes of the tests are obtained by Monte Carlo simulation. Through a simulation study, power values of the tests are compared with each other. Finally, an illustrative example is presented and analyzed.

We have examined the convergence behavior of the LSCMA in some simple environments. Algorithms such as Multi Target CMA, Multistage CMA, and Iterative Least Squares with Projection can be used for this purpose. The results presented here can form a basis for analysis of these multi-signal extraction techniques. Clearly, the variance and distribution of output SINR obtained with the LSCMA is also an important area for investigation. We finally comment on the hard-limit non-linearity. For high SIR, the hard-limiter is the optimal non-linearity when the desired signal has a constant envelope. However, at low SIR other non-linearities can yield greater SIR gain. Thus, it is possible that non-linear functions other than the hard-limit can be used to develop blind adaptive algorithms, which converge faster for low initial SINR.

The Inverse Gaussian distribution finds application in various fields, such as finance, survival analysis, psychology, engineering, physics, and quality control. Its capability to model skewed distributions and non-constant hazard rates makes it a valuable tool for understanding a wide range of phenomena. In this paper, we present a goodness-of-fit test specifically designed for the Inverse Gaussian distribution. Our test uses an estimate of the Gini index, a statistical measure of inequality. We provide comprehensive details on the exact and asymptotic distributions of the newly developed test statistic. To facilitate the application of the test, we estimate the unknown parameters of the Inverse Gaussian distribution using maximum likelihood estimators. Monte Carlo methods are utilized to determine the critical points and assess the actual sizes of the test. A power comparison study is conducted to evaluate the performance of existing tests. Comparing its powers with those of other tests, we demonstrate that the Gini index-based test performs favorably. Finally, we present a real data analysis for illustrative purposes.

In this paper, a Bayesian approach is proposed for shift point detection in an inverse Gaussian distribution. In this study, the mean parameter of inverse Gaussian distribution is assumed to be constant and shift points in shape parameter is considered. First the posterior distribution of shape parameter is obtained. Then the Bayes estimators are derived under a class of priors and using various loss functions. We assumed uniform, Jeffreys, exponential, gamma and chi square distributions as prior distributions. The squared error loss function (SELF), entropy loss function (ELF), linex loss function (LLF) and precautionary loss function (PLF), are used as loss functions. We attempt to find out the best estimator for shift point under various priors and loss functions. The proposed Bayesian approach can be adapted to any similar problem for shift point detection. Simulation studies were done to investigate the performance of different loss functions. The results of simulation study denote that the Jeffrey prior distribution under PLF has the most accurate estimation of shift point for sample size of 20, and the gamma prior distribution under SELF has the most accurate estimation of shift point for sample size of 50.