Characterization of generalized Gamma-Lindley distribution using truncated moments of order statistics

2021 ◽  
Vol 71 (2) ◽  
pp. 455-474
Author(s):  
Dorsaf Laribi ◽  
Afif Masmoudi ◽  
Imen Boutouria
Keyword(s):  
Order Statistics ◽  
Survival Function ◽  
Lindley Distribution ◽  
Underlying Distribution ◽  
First Order ◽  
New Class ◽  
Generalized Gamma ◽  
Special Cases ◽  
Two Parameters

Abstract Having only two parameters, the Gamma-Lindley distribution does not provide enough flexibility for analyzing different types of lifetime data. From this perspective, in order to further enhance its flexibility, we set forward in this paper a new class of distributions named Generalized Gamma-Lindley distribution with four parameters. Its construction is based on certain mixtures of Gamma and Lindley distributions. The truncated moment, as a characterization method, has drawn a little attention in the statistical literature over the great popularity of the classical methods. We attempt to prove that the Generalized Gamma-Lindley distribution is characterized by its truncated moment of the first order statistics. This method rests upon finding a survival function of a distribution, that is a solution of a first order differential equation. This characterization includes as special cases: Gamma, Lindley, Exponential, Gamma-Lindley and Weighted Lindley distributions. Finally, a simulation study is performed to help the reader check whether the available data follow the underlying distribution.

THEORETICAL PROPERTIES OF THE WEIGHTED GENERALIZED GAMMA AND RELATED DISTRIBUTIONS

2015 ◽  
Vol 29 (3) ◽  
pp. 421-432 ◽  
Author(s):  
Hewa A. Priyadarshani ◽  
Broderick O. Oluyede
Keyword(s):  
Gamma Distribution ◽  
Hazard Function ◽  
Gamma Model ◽  
Generalized Gamma Distribution ◽  
New Class ◽  
Generalized Gamma ◽  
Special Cases ◽  
Entropy Measures ◽  
Skewness Coefficient ◽  
Coefficient Of Skewness

A new class of weighted generalized gamma distribution (WGGD) and related distributions are presented. Theoretical properties of the generalized gamma model, WGGD including the hazard function, reverse hazard function, moments, coefficient of variation, coefficient of skewness, coefficient of kurtosis, and entropy measures are derived. The results presented here generalizes the generalized gamma distribution and includes several distributions as special cases. The special cases include generalized gamma, weighted gamma, weighted exponential, weighted Weibull, weighted Rayleigh distributions, and their underlying or parent distributions.

Turing machines and the spectra of first-order formulas

1974 ◽  
Vol 39 (1) ◽  
pp. 139-150 ◽  
Author(s):  
Neil D. Jones ◽  
Alan L. Selman
Keyword(s):  
Order Logic ◽  
Automata Theory ◽  
Turing Machines ◽  
First Order ◽  
Context Sensitive ◽  
Open Questions ◽  
Special Cases ◽  
Computational Aspects ◽  
The Difference

H. Scholz [11] defined the spectrum of a formula φ of first-order logic with equality to be the set of all natural numbers n for which φ has a model of cardinality n. He then asked for a characterization of spectra. Only partial progress has been made. Computational aspects of this problem have been worked on by Gunter Asser [1], A. Mostowski [9], and J. H. Bennett [2]. It is known that spectra include the Grzegorczyk class and are properly included in . However, no progress has been made toward establishing whether spectra properly include , or whether spectra are closed under complementation.A possible connection with automata theory arises from the fact that contains just those sets which are accepted by deterministic linear-bounded Turing machines (Ritchie [10]). Another resemblance lies in the fact that the same two problems (closure under complement, and proper inclusion of ) have remained open for the class of context sensitive languages for several years.In this paper we show that these similarities are not accidental—that spectra and context sensitive languages are closely related, and that their open questions are merely special cases of a family of open questions which relate to the difference (if any) between deterministic and nondeterministic time or space bounded Turing machines.In particular we show that spectra are just those sets which are acceptable by nondeterministic Turing machines in time 2cx, where c is constant and x is the length of the input. Combining this result with results of Bennett [2], Ritchie [10], Kuroda [7], and Cook [3], we obtain the “hierarchy” of classes of sets shown in Figure 1. It is of interest to note that in all of these cases the amount of unrestricted read/write memory appears to be too small to allow diagonalization within the larger classes.

scholarly journals Diagonal sections of copulas, multivariate conditional hazard rates and distributions of order statistics for minimally stable lifetimes

2021 ◽  
Vol 9 (1) ◽  
pp. 394-423
Author(s):  
Rachele Foschi ◽  
Giovanna Nappo ◽  
Fabio L. Spizzichino
Keyword(s):  
Order Statistics ◽  
Hazard Rate ◽  
Joint Distribution ◽  
Survival Function ◽  
Hazard Rates ◽  
Archimedean Copulas ◽  
Absolutely Continuous ◽  
Marginal Distributions ◽  
Special Cases ◽  
Survival Copula

Abstract As a motivating problem, we aim to study some special aspects of the marginal distributions of the order statistics for exchangeable and (more generally) for minimally stable non-negative random variables T 1, ..., Tr. In any case, we assume that T 1, ..., Tr are identically distributed, with a common survival function ̄G and their survival copula is denoted by K. The diagonal sections of K, along with ̄G, are possible tools to describe the information needed to recover the laws of order statistics. When attention is restricted to the absolutely continuous case, such a joint distribution can be described in terms of the associated multivariate conditional hazard rate (m.c.h.r.) functions. We then study the distributions of the order statistics of T 1, ..., Tr also in terms of the system of the m.c.h.r. functions. We compare and, in a sense, we combine the two different approaches in order to obtain different detailed formulas and to analyze some probabilistic aspects for the distributions of interest. This study also leads us to compare the two cases of exchangeable and minimally stable variables both in terms of copulas and of m.c.h.r. functions. The paper concludes with the analysis of two remarkable special cases of stochastic dependence, namely Archimedean copulas and load sharing models. This analysis will allow us to provide some illustrative examples, and some discussion about peculiar aspects of our results.

ASYMPTOTIC EXPANSIONS OF GENERALIZED QUANTILES AND EXPECTILES FOR EXTREME RISKS

2015 ◽  
Vol 29 (3) ◽  
pp. 309-327 ◽  
Author(s):  
Tiantian Mao ◽  
Kai Wang Ng ◽  
Taizhong Hu
Keyword(s):  
Value At Risk ◽  
Risk Measures ◽  
Domain Of Attraction ◽  
Random Variable ◽  
Second Order ◽  
Underlying Distribution ◽  
First Order ◽  
Extreme Risk ◽  
Special Cases ◽  
Extreme Risks

Generalized quantiles of a random variable were defined as the minimizers of a general asymmetric loss function, which include quantiles, expectiles and M-quantiles as their special cases. Expectiles have been suggested as potentially better alternatives to both Value-at-Risk and expected shortfall risk measures. In this paper, we first establish the first-order expansions of generalized quantiles for extreme risks as the confidence level α↑ 1, and then investigate the first-order and/or second-order expansions of expectiles of an extreme risk as α↑ 1 according to the underlying distribution belonging to the max-domain of attraction of the Fréchet, Weibull, and Gumbel distributions, respectively. Examples are also presented to examine whether and how much the first-order expansions have been improved by the second-order expansions.

CHARACTERIZATION ORDERING RESULTS FOR LARGEST ORDER STATISTICS FROM HETEROGENEOUS AND HOMOGENEOUS EXPONENTIATED GENERALIZED GAMMA VARIABLES

2018 ◽  
Vol 33 (3) ◽  
pp. 460-470 ◽  
Author(s):  
Abedin Haidari ◽  
Amir T. Payandeh Najafabadi
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Hazard Rate ◽  
Random Variables ◽  
Reversed Hazard Rate ◽  
Generalized Gamma

The main aim of this paper is to present two new results concerning the characterization of likelihood ratio and reversed hazard rate orders between largest order statistics from two sets of independent heterogeneous and homogeneous exponentiated generalized gamma distributed random variables. These characterization results complete and strengthen some previous ones in the literature.

scholarly journals Weighted Cumulative Residual (Past) Inaccuracy For Minimum (Maximum) of Order Statistics

2020 ◽  
Vol 8 (1) ◽  
pp. 110-126
Author(s):  
Safeih Daneshi ◽  
Ahmad Nezakati ◽  
Saeid Tahmasebi
Keyword(s):  
Order Statistics ◽  
Linear Transformation ◽  
Order Statistic ◽  
Survival Function ◽  
Stochastic Ordering ◽  
First Order ◽  
Properties And Characterization ◽  
Parent Distribution ◽  
Cumulative Residual

In this paper, we propose a measure of weighted cumulative residual inaccuracy between survival function of the first-order statistic and parent survival function $\bar{F}$. We also consider weighted cumulative inaccuracy measure between distribution of the last- order statistic and parent distribution $F$. For these concepts, we obtain some reliability properties and characterization results  such as relationships with other functions, bounds, stochastic ordering and effect of linear transformation. Dynamic versions of these weighted measures are considered.

scholarly journals Non Bayesian estimation for survival and hazard function of weighted Rayleigh distribution (b)

2020 ◽  
pp. 3059-3071
Author(s):  
Saad Adnan Zain
Keyword(s):  
Hazard Function ◽  
Shape Parameter ◽  
Survival Function ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Likelihood Method ◽  
Data Sets ◽  
New Class ◽  
The Moment ◽  
Two Parameters

In this paper, we proposed a new class of Weighted Rayleigh Distribution based on two parameters, one is scale parameter and the other is shape parameter which introduced in Rayleigh distribution. The main properties of this class are derived and investigated in . The moment method and maximum likelihood method are used to obtain estimators of parameters, survival function and hazard function. Real data sets are collected to investigate two methods which depend it in this study. A comparison was made between two methods of estimation.

Targeting IDH Mutations in AML: Wielding the Double-edged Sword of Differentiation

2020 ◽  
Vol 20 (7) ◽  
pp. 490-500 ◽  
Author(s):  
Justin S. Becker ◽  
Amir T. Fathi
Keyword(s):  
Genome Structure ◽  
Cellular Metabolism ◽  
Standard Of Care ◽  
Competitive Inhibitor ◽  
Driver Mutations ◽  
New Class ◽  
Regulatory Enzymes ◽  
Idh Mutations ◽  
Genomic Characterization

The genomic characterization of acute myeloid leukemia (AML) by DNA sequencing has illuminated subclasses of the disease, with distinct driver mutations, that might be responsive to targeted therapies. Approximately 15-23% of AML genomes harbor mutations in one of two isoforms of isocitrate dehydrogenase (IDH1 or IDH2). These enzymes are constitutive mediators of basic cellular metabolism, but their mutated forms in cancer synthesize an abnormal metabolite, 2- hydroxyglutarate, that in turn acts as a competitive inhibitor of multiple gene regulatory enzymes. As a result, leukemic IDH mutations cause changes in genome structure and gene activity, culminating in an arrest of normal myeloid differentiation. These discoveries have motivated the development of a new class of selective small molecules with the ability to inhibit the mutant IDH enzymes while sparing normal cellular metabolism. These agents have shown promising anti-leukemic activity in animal models and early clinical trials, and are now entering Phase 3 study. This review will focus on the growing preclinical and clinical data evaluating IDH inhibitors for the treatment of IDH-mutated AML. These data suggest that inducing cellular differentiation is central to the mechanism of clinical efficacy for IDH inhibitors, while also mediating toxicity for patients who experience IDH Differentiation Syndrome. Ongoing trials are studying the efficacy of IDH inhibitors in combination with other AML therapies, both to evaluate potential synergistic combinations as well as to identify the appropriate place for IDH inhibitors within existing standard-of-care regimens.

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