Search

In this article, we propose a Gompertz-two-parameter-Lindley distribution by mixing the frailty parameter of the Gompertz distribution with a two-parameter Lindley distribution. The structural properties of the model, such as shape properties, cumulative distribution, quantile functions, moment, moment generating function, failure rate function, mean residual function, and stochastic orders, were derived. Moreover, the unknown parameters are estimated by the profile log likelihood algorithm, and their performance is examined by simulation studies. Finally, a real data example is used to demonstrate the application of the proposed model.

A common and important problem in medicine, economics and environmental studies is the comparison of the variances of several treatments with that of a control treatment. Among the existing methods, Spurrier's optimal test based on multivariate F distribution has exact type I error rates. However, it requires equal sample sizes among the treatment groups. To extend the application scope, in this paper, we propose a new efficient test for comparing several variances with a control using the marginal inferential model (MIM). Simulation studies show that the MIM test guarantees the exact type I error rate whether the sample size is equal or unequal. Moreover, the power of the MIM test is competitive with that of Spurrier's optimal test. Finally, two real examples are used to demonstrate the application of the proposed method. [ABSTRACT FROM AUTHOR]

Due to the discrete nature and parameter constraints, the interval estimation of a Poisson parameter with background has been a challenging problem in statistics. Among the existing good methods, the FC interval, RW interval, G interval, MS interval, and EB interval have conservative coverage probability in our simulation study. In this paper, we propose a randomized confidence interval (CI) for a constrained Poisson parameter based on the inferential model (IM) and suggest the practical use of its nonrandomized approximation. The randomized IM CI is proven to guarantee the exact coverage probability, and our nonrandomized approximation has coverage closer to the confidence coefficient than the existing CIs in most cases. Moreover, our nonrandomized interval always has the shortest expected length among the six CIs. Finally, a real example is used to demonstrate the application of the proposed methods. [ABSTRACT FROM AUTHOR]

In drug development, non inferiority tests are often employed to determine the odds ratio between two independent binomial proportions. Some traditional test statistics for non inferiority based on different statistical schools of thought are available, but they can produce markedly different behaviors. Cornfield's exact conditional test is criticized for its conservativeness, while the Wald and score tests may be applicable for large samples but tend to be liberal with small samples. Although the mid-p value method has recently gained wide acceptance for its better behavior than those of other tests, it has almost no solid theoretical foundation attached to it. In the view of the fiducial school of thought, the fiducial test based on Fisher's fiducial argument also tends to perform unsatisfactorily for small samples. In this paper, we suggest an IM-based efficient test using the randomized plausibility function based on the Inferential Model. We prove that our new method is not only valid but also efficient, i.e., it maintains a nominal type I error rate, and we show, via simulations, that the proposed test also has satisfactory power when compared with those of other competing tests. A numerical example illustrates the proposed method. [ABSTRACT FROM AUTHOR]

Non-inferiority of one treatment to another based on odds ratio for the matched-pair design is a common issue in the medical research. Liu et al. derived two asymptotic tests, delta method and score test, which can be applicable for large samples but may tend to be liberal for small sample sizes. Jin et al. proposed an IM-based method that can control the type I risk well but may be somewhat conservative. In this paper, we extend the IM-based method to RIM-based test using the randomized plausibility function. We prove that our new proposed method is not only valid but also efficient. Simulation studies confirm that the RIM-based test is better than other methods. A numerical example illustrates the proposed method. [ABSTRACT FROM AUTHOR]

Hida and Tango established a statistical testing framework for the three-arm non-inferiority trial including a placebo with a pre-specified non-inferiority margin to overcome the shortcomings of traditional two-arm non-inferiority trials (such as having to choose the non-inferiority margin). In this paper, we propose a new method that improves their approach with respect to two aspects. We construct our testing statistics based on the best unbiased pooled estimators of the homogeneous variance; and we use the principle of intersection-union tests to determine the rejection rule. We theoretically prove that our test is better than that of Hida and Tango for large sample sizes. Furthermore, when that sample size was small or moderate, our simulation studies showed that our approach performed better than Hida and Tango's. Although both controlled the type I error rate, their test was more conservative and the statistical power of our test was higher. [ABSTRACT FROM AUTHOR]

Hida and Tango established a statistical testing framework for the three-arm non-inferiority trial including a placebo with a pre-specified non-inferiority margin to overcome the shortcomings of traditional two-arm non-inferiority trials (such as having to choose the non-inferiority margin). In this paper, we propose a new method that improves their approach with respect to two aspects. We construct our testing statistics based on the best unbiased pooled estimators of the homogeneous variance; and we use the principle of intersection-union tests to determine the rejection rule. We theoretically prove that our test is better than that of Hida and Tango for large sample sizes. Furthermore, when that sample size was small or moderate, our simulation studies showed that our approach performed better than Hida and Tango's. Although both controlled the type I error rate, their test was more conservative and the statistical power of our test was higher.