In probability theory and statistics , the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable. The support is defined by the two parameters, a and b , which are its minimum and maximum values. The distribution is often abbreviated U a , b. It is the maximum entropy probability distribution for a random variable X under no constraint other than that it is contained in the distribution's support. The probability density function of the continuous uniform distribution is:.
Uniform Probability density function. In symbols. Criterion validity involves a comparison of the single data Uniform data definition assessment with that obtained using a gold standard procedure. In the context of probability distributionsuniform distribution refers to a probability distribution for which all of the values that a random variable can take definituon occur with equal probability. Consensus development methods, and their use in clinical guideline development. Following the publication of the Utstein Template dsta Uniform Reporting of Data Following Major Trauma Utstein Trauma Templatewe performed a study on the feasibility of collecting core data from registries that had implemented the template [ 29 ], which Uniform data definition important feedback to a Dried seaweed flavor strips process. Population Covered:. The variance second central moment is:. One of the first consensus-based templates published for use in critical care was uniform documenting and reporting of data for out-of-hospital cardiac arrest, which was published in by a task force preceding a conference at Utstein Abbey, Stavanger, Norway [ 17 ]. Uniform Distribution.
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The uniform Uniform data definition, definitino to Socialism, is like so many other imputations, sheer nonsense. Take the quiz Where in the World? Non-uniform distribution peaks and valleys. Law enforcement agencies also report the number of crime cases cleared. Headquarters: Robert F. ET, Monday - Friday except federal holidays. Can you spell these 10 commonly misspelled words? Spanish Central: Translation of uniform. Britannica English: Translation of uniform for Arabic Speakers. Enter your email for updates:. Uniform communications code word. First Known Use of uniform Adjective 15th century, in the meaning defined at sense 1 Verb circain the meaning defined at sense 1 Nounin the meaning Uniform data definition above Communications code wordin the Uniorm defined above. The Unifork of Recording menstrual cycles toss is a random variable that can take on any of six possible values: 1, 2, 3, 4, 5, or 6. Federal law enforcement.
- His uniform was too tight and was wrapped around his doughy body like cellophane.
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- In statistics, a type of probability distribution in which all outcomes are equally likely; each variable has the same probability that it will be the outcome.
Clinical practice in trauma and critical care is predominantly derived from quantitative observational cohort studies based on data retrospectively collected from medical records.
Such data create uncontrolled bias and influence external and internal validity, thereby hindering systematic reviews. Templates or standards for uniform documenting and scientific reporting may result in high quality and internationally standardised data being collected on a regular basis, enhance large international multi-centre studies, and increase the quality of evidence.
Templates or standards may be developed using multidisciplinary expert panel consensus methods. We present three consensus processes aimed at developing templates for documenting and scientific reporting. The template preparation was based on expert panel consensus derived through a modified nominal group technique NGT method that combined the traditional Delphi method with the traditional NGT method in a four-step process. Standard templates for documenting and scientific reporting were developed for major trauma, pre-hospital advanced airway handling, and physician-staffed pre-hospital EMS.
All templates were published in scientific journals. Our modified NGT consensus method can successfully be used to establish templates for reporting trauma and critical care data. When used in a structured manner, the method uses recognised experts to achieve consensus, but based on our experiences, we recommend the consensus process to be followed by feasibility, reliability, and validity testing.
Current clinical critical care practice is, to varying degrees, evidence based. Evidence-based practice is commonly derived from reports published in international registries and libraries e. Although RCTs are considered the gold standard for medical research, ethical, legal, and practical aspects limit the establishment of sound RCT protocols in critical care.
Critical care patients are, by definition, rarely amenable to informed consent, and there is a consequent lack of RCTs in this field of medicine [ 2 ]. The scientific reports in critical care are predominantly based on quantitative observational cohort studies and animal studies [ 3 ]. They typically require much lower funding levels. Prospective observational studies are valuable alternatives to RCTs and will continue to supply crucial scientific evidence.
The quality of data collected routinely for other purposes may be of variable quality [ 4 , 5 ]. Even in cases in which the data quality is satisfactory, data that are defined and collected for other purposes can create uncontrolled bias and influence external and internal validity [ 6 , 7 ].
This point is well illustrated by the recently published ERC Guidelines for cardiopulmonary resuscitation and emergency cardiovascular care, which are substantially based on low-level evidence. Observational studies constitute a significant proportion of the reference list [ 12 ].
This process ranks RCTs highly, but they are uncommon, often inconclusive non-significant , and rarely provide sufficient evidence to construct a robust guideline. A primary challenge to researchers and clinicians has been to improve the quality of observational data collected in day-to-day practice. One method is to develop templates or standards to uniformly document and report data.
A template or standard ensures that the reported variables in specific patient groups, specific emergency medical conditions, and from specific interventions are consistent and reproducible. Such standardised variables with precise definitions may strengthen the quality of routinely collected data and the validity of published reports, thereby facilitating the analysis of reports in producing systematic reviews. High quality, well defined, and internationally standardised data that are collected regularly might enhance large international multi-centre studies and increase the quality of evidence [ 13 ].
Templates or standards for documenting and reporting data may be developed using qualitative methods, such as multidisciplinary expert panel consensus methods [ 14 , 15 ]. There is an acceptance and tradition for using formal consensus development methods to examine the appropriateness of clinical interventions, to develop guidelines for diagnosing and treating specific diseases, to identify education and research priorities, and to facilitate studies on preventable deaths because of problems in patient care [ 1 , 16 ].
Consensus development methods allow a combination of evidence-based knowledge, personal experience, and general insight into the characteristics of the patient cohort assessed or problem addressed. Critical steps following the development of templates for documenting and reporting event data is the implementation of the agreed data variables in existing registries, and securing the reliability and validity of the defined data variables.
One of the first consensus-based templates published for use in critical care was uniform documenting and reporting of data for out-of-hospital cardiac arrest, which was published in by a task force preceding a conference at Utstein Abbey, Stavanger, Norway [ 17 ]. The three processes aimed to develop templates for documenting and reporting data for scientific purposes.
The Delphi method has been widely used in health care research for defining priorities in education, clinical practice, organisation, and planning. It is commonly based on three e-mail rounds in which a large number of experts provide opinions on specific matters.
The opinions are grouped and re-circulated for ranking, and again summarised and circulated for a re-ranking based on the individual experts' insights in the group response. The meeting is divided into separate rounds, in which the experts propose, rate, discuss, and re-rate a list of items, variables, or questions.
The discussions are facilitated by an expert or non-expert who is highly familiar with the method. Consensus is reached by the end of the meeting. The preparation of the three templates referred to in this paper was based on a modified NGT method that combines the traditional Delphi method with the traditional NGT method.
The entire process consisted of four steps. The first part of the consensus process step one and two uses the Delphi method approach to allow the experts to identify data variables relevant for the template under development.
To fully utilise the clinical and scientific competence of the experts, they are allowed to interact by applying the NGT method step three and four. In the first step, each expert was supplied with the necessary background documents i. The expert was asked to return by e-mail the proposals for inclusion and exclusion criteria, a set maximum number of core data variables in a prioritised order, and optional data variables that were regarded as important for the template preparation. The proposed variables were divided into set variable subgroups.
A maximum number of core variables were defined by the co-ordinating project group prior to each process, with the intention of keeping the expert panel focused on the core data. These initial proposals were aggregated and systemised by the co-ordinating project group according to the frequency with which the variable had been proposed by the experts. The third step consisted of one or two consensus meetings in which the members of the expert panels, in groups and plenary sessions, discussed their views in a structured way and reached their conclusions.
The consensus meeting differed significantly in structure from the e-mail rounds. During the meeting, the discussion was open, allowing interactions between the panel members to influence the ranking and conclusions, including novel variables if agreed upon.
Exceeding the set maximum number of variables was allowed pending group approval. In the fourth step, based on the conclusions from the consensus meeting s , the co-ordinating project group edited a final proposal for a template, upon which the experts were allowed to comment by e-mail. To complete the process, a letter of agreement was signed by all the expert panel members to enhance the implementation of the achieved template in the daily documentation of practice.
Three international expert panels were selected to participate in these three Utstein processes. Because of the structure of the consensus meeting, a maximum number of twenty experts per process were set. The experts were identified by Google and PubMed searches on the subject, through personal networks of the co-ordinating project group, and by recommendations from previously selected members.
The invited experts who could not attend were asked to suggest a substitute colleague. Three reminders were sent to the non-responders. In the e-mail rounds, the experts were supplied with a spreadsheet that was designed as a template for the proposals. Each variable required additional information on the exact data variable definition, the possible data variable categories, and the data variable source e.
After each round, the experts returned their completed spreadsheets of proposals to the co-ordinating project group. In step three of the modified NGT method, the expert panel gathered at a two-day meeting and agreed on the inclusion and exclusion criteria and a core data set for the template.
Two experienced scientists and clinicians who were familiar with the method facilitated the meeting of each of the three Utstein processes.
In a first plenary section, the co-ordinating project group presented the proposed variables from step two, and the facilitators presented the set structure for the meeting. The experts were divided into two groups and separately discussed the specific inclusion and exclusion criteria and variables for the proposed dataset. The groups subsequently presented their discussions in plenary sessions, at which all variables were discussed, debated, and agreed upon.
On day two, the variables were given precise definitions and categorised in a plenary session. In two of the consensus meetings [ 7 , 24 ], the project group allowed a few variables to not be accompanied by specific definitions during the meeting, authorising the co-ordinating project group to propose final definitions to be decided during step four of the consensus process.
The expert panels achieved consensus during the planned four steps in all three Utstein processes. The structure of each process differed slightly. Twenty-three experts were invited, and 19 accepted the invitation and joined the Utstein process. In , the expert panel was asked to propose inclusion and exclusion criteria, as well as a maximum of 30 core data variables in a prioritised order.
In step three, the expert group did not reach consensus on all variables because of extensive discussions and a prolonged decision process. To finalise the process, the expert group decided to conduct a second consensus meeting.
During these two consensus meetings, which were held at the Utstein Abbey in May and December , the panellists discussed their views by a structured method and reached consensus. Of the 19 individuals participating in the e-mail process, 18 participated in the first consensus meeting and 16 in the second meeting. No formal communication regarding this process occurred among the experts between the two meetings.
After completing the process, the expert panel had agreed upon the inclusion and exclusion criteria, 36 core data variables and four subsidiary variables for the template.
The co-ordinating project group published a data definition catalogue on a dedicated web site with open access. In January , 15 experts accepted invitations to join the Utstein process. The panel was asked to propose 10 core data variables and five optional variables in a prioritised order. During the consensus meeting at Utstein Abbey in April , the expert panel agreed that any patient receiving advanced airway management, defined as the attempted insertion of an advanced airway adjunct or administration of ventilatory assistance, should meet the inclusion criteria.
The expert panel agreed that advanced airway management during inter-hospital transfer should be excluded. The expert panel agreed on 23 core data variables that were divided into three groups: system, patient, and post-intervention. In winter , an expert panel was invited and asked to propose inclusion and exclusion criteria, as well as a maximum of 50 core data variables in a prioritised order. Seventeen experts were invited, and 16 accepted the invitation and joined the Utstein process.
The final core data set was sent to the experts by email after the meeting, and the experts were allowed to make comments to the final data set. A few minor changes, which were mainly related to data definitions, were made at this point. The difficulty of comparing trauma and critical care between centres and over time based on locally defined data variables has been illustrated in several recent reports [ 6 - 8 , 28 ]. Over the last two decades, several templates for standardised documentation and reporting in critical care have been published.
These templates have proven valuable, particularly in the field of cardiac arrest research, in comparing the activity, effect, and efficiency of health care systems. Traditionally, such templates have been designed using consensus methods. In this paper, we present a modified NGT method used in three consensus processes with the aim of developing templates for reporting from three specific areas of trauma and critical care.
We perceived a number of benefits from the use of this modified NGT method to reach consensus. A consensus process derives its credibility, in part, from the composition of the expert panel. In these three consensus processes, the experts were professional authorities who were key stakeholders in their services and respected representatives of their profession.
They had significant scientific credibility within their fields of medicine. The initial proposals from the experts were unconfined by the group dynamics.
How Binomial Distribution Works The binomial distribution is a probability distribution that summarizes the likelihood that a value will take one of two independent values. The result of these conferences was the release of a Blueprint for the Future of the Uniform Crime Reporting Program release in May , detailing the necessary revisions. This report details the number of actual crimes of each type in the Return A and the monetary value of property stolen in conjunction with that crime. What is Uniform Distribution? Joint probability is the probability of event Y occurring at the same time that event X occurs. Each of these outcomes is equally likely to occur.
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Do you know the person or title these quotes describe? Uniform communications code word. Examples of uniform in a Sentence Adjective The museum is kept at a uniform temperature to protect the artifacts.
All departments have uniform training standards. Noun the band uniform was brown with red and white stripes. Joseph: No. First Known Use of uniform Adjective 15th century, in the meaning defined at sense 1 Verb circa , in the meaning defined at sense 1 Noun , in the meaning defined above Communications code word , in the meaning defined above. Resources for uniform Time Traveler! Explore the year a word first appeared. Dictionary Entries near uniform uniflow engine unifoliate unifoliolate uniform Uniform uniformal uniform flow.
Phrases Related to uniform in full uniform. Other Words from uniform uniformly adverb The trees are uniformly spaced. Comments on uniform What made you want to look up uniform? Get Word of the Day daily email! Test Your Vocabulary. Love words? A linguistic analysis of a notorious pronunciation On Contractions of Multiple Words You all would not have guessed some of these Literally How to use a word that literally drives some people nuts.
Is Singular 'They' a Better Choice? Word Games Word Puzzles Challenge yourself with these word puzzles. Take the quiz Where in the World? A Quiz Do you know what languages these words come from? Take the quiz Spell It Can you spell these 10 commonly misspelled words? Take the quiz Citation Do you know the person or title these quotes describe? This probability distribution is defined as follows.
Consider the toss of a single die. The outcome of this toss is a random variable that can take on any of six possible values: 1, 2, 3, 4, 5, or 6. Each of these outcomes is equally likely to occur. Therefore, the outcome from the toss of a single die has a uniform distribution. The term "uniform distribution" is also used to describe the shape of a graph that plots observed values in a set of data.
Graphically, when the observed values in a set of data are equally spread across the range of the data set, the distribution is also called a uniform distribution. Graphically, a uniform distribution has no distinct peaks.
Uniform Distribution: Definition
In probability theory and statistics , the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable.
The support is defined by the two parameters, a and b , which are its minimum and maximum values. The distribution is often abbreviated U a , b. It is the maximum entropy probability distribution for a random variable X under no constraint other than that it is contained in the distribution's support. The probability density function of the continuous uniform distribution is:.
The latter is appropriate in the context of estimation by the method of maximum likelihood. Also, it is consistent with the sign function which has no such ambiguity. The cumulative distribution function is:. The moment-generating function is: .
The mean first moment of the distribution is:. The variance second central moment is:. Let X k be the k th order statistic from this sample. The expected value is. The probability that a uniformly distributed random variable falls within any interval of fixed length is independent of the location of the interval itself but it is dependent on the interval size , so long as the interval is contained in the distribution's support.
One interesting property of the standard uniform distribution is that if u 1 has a standard uniform distribution, then so does 1-u 1. This property can be used for generating antithetic variates , among other things. As long as the same conventions are followed at the transition points, the probability density function may also be expressed in terms of the Heaviside step function :. There is no ambiguity at the transition point of the sign function.
Using the half-maximum convention at the transition points, the uniform distribution may be expressed in terms of the sign function as:. In statistics , when a p-value is used as a test statistic for a simple null hypothesis , and the distribution of the test statistic is continuous, then the p-value is uniformly distributed between 0 and 1 if the null hypothesis is true.
There are many applications in which it is useful to run simulation experiments. Many programming languages come with implementations to generate pseudo-random numbers which are effectively distributed according to the standard uniform distribution. The uniform distribution is useful for sampling from arbitrary distributions. A general method is the inverse transform sampling method, which uses the cumulative distribution function CDF of the target random variable.
This method is very useful in theoretical work. Since simulations using this method require inverting the CDF of the target variable, alternative methods have been devised for the cases where the cdf is not known in closed form.
One such method is rejection sampling. The normal distribution is an important example where the inverse transform method is not efficient. However, there is an exact method, the Box—Muller transformation , which uses the inverse transform to convert two independent uniform random variables into two independent normally distributed random variables. In analog-to-digital conversion a quantization error occurs.
This error is either due to rounding or truncation. When the original signal is much larger than one least significant bit LSB , the quantization error is not significantly correlated with the signal, and has an approximately uniform distribution. The RMS error therefore follows from the variance of this distribution. This follows for the same reasons as estimation for the discrete distribution , and can be seen as a very simple case of maximum spacing estimation. This problem is commonly known as the German tank problem , due to application of maximum estimation to estimates of German tank production during World War II.
The maximum likelihood estimator is given by:. The method of moments estimator is given by:. Although both the sample mean and the sample median are unbiased estimators of the midpoint, neither is as efficient as the sample mid-range , i.
In symbols. From Wikipedia, the free encyclopedia. Uniform Probability density function. Main article: Inverse transform sampling. Main article: Quantization error. Main article: German tank problem. Journal of Econometrics. Transport and Telecommunication 3 1 Probability distributions. Benford Bernoulli beta-binomial binomial categorical hypergeometric Poisson binomial Rademacher soliton discrete uniform Zipf Zipf—Mandelbrot.
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