In this paper, we introduce a new four-parameter generalized version of the Gompertz model which is called Beta-Gompertz (BG) distribution. It includes some well-known lifetime distributions such as Beta-exponential and generalized Gompertz distributions as special sub-models. This new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a decreasing, increasing, and bathtub-shaped failure rate function depending on its parameters. Some mathematical properties of the new distribution, such as closed-form expressions for the density, cumulative distribution, hazard rate function, the kth order moment, moment generating function, Shannon entropy, and the quantile measure are provided. We discuss maximum likelihood estimation of the BG parameters from one observed sample and derive the observed Fisher's information matrix. A simulation study is performed in order to investigate the properties of the proposed estimator. At the end, in order to show the BG distribution flexibility, an application using a real data set is presented.
This study compared a new regimen (group A: doxycycline, co-amoxiclav, omeprazole) and two routinely prescribed regimens (group B: amoxicillin, omeprazole, furazolidone, bismuth; group C: amoxicillin, clarithromycin, omeprazole) to find an acceptable first-line treatment option for Helicobacter pylori. The study population consisted of 189 patients who referred to our clinic to undergo endoscopy due to ulcer-like dyspepsia. The H. pylori eradication rate was 68% in group A, 56% in group B, and 70% in group C according to per-control analysis. There was no statistically significant difference in H. pylori eradication between groups A and B (P = 0.187), groups A and C (P = 0.857), and groups B and C (P = 0.15). In conclusion, although none of the three eradication regimens can be recommended as a first-line eradication treatment, the new regimen is at least as effective and probably better tolerated than the two routinely applied regimens.
We introduce in this paper a new class of distributions which generalizes the linear failure rate (LFR) distribution and is obtained by compounding the LFR distribution and power series (PS) class of distributions. This new class of distributions is called the linear failure rate-power series (LFRPS) distributions and contains some new distributions such as linear failure rate geometric (LFRG) distribution, linear failure rate Poisson (LFRP) distribution, linear failure rate logarithmic (LFRL) distribution, linear failure rate binomial (LFRB) distribution and Raylight-power series (RPS) class of distributions. Some former works such as exponential-power series (EPS) class of distributions, exponential geometric (EG) distribution, exponential Poisson (EP) distribution and exponential logarithmic (EL) distribution are special cases of the new proposed model.The ability of the LFRPS class of distributions is in covering five possible hazard rate function i.e., increasing, decreasing, upside-down bathtub (unimodal), bathtub and increasing-decreasing-increasing shaped. Several properties of the LFRPS distributions such as moments, maximum likelihood estimation procedure via an EM-algorithm and inference for a large sample, are discussed in this paper. In order to show the flexibility and potentiality of the new class of distributions, the fitted results of the new class of distributions and some its submodels are compared using a real data set.
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