Average Probability Error
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removed. (December 2009) (Learn how and when to remove this template message) In statistics, the term "error" arises in two ways. Firstly, it average probability density function arises in the context of decision making, where the probability of error
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may be considered as being the probability of making a wrong decision and which would have a
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different value for each type of error. Secondly, it arises in the context of statistical modelling (for example regression) where the model's predicted value may be in error regarding
Probability Of Error In Mmse Multiuser Detection
the observed outcome and where the term probability of error may refer to the probabilities of various amounts of error occurring. Hypothesis testing[edit] In hypothesis testing in statistics, two types of error are distinguished. Type I errors which consist of rejecting a null hypothesis that is true; this amounts to a false positive result. Type II errors which probability of error bpsk consist of failing to reject a null hypothesis that is false; this amounts to a false negative result. The probability of error is similarly distinguished. For a Type I error, it is shown as α (alpha) and is known as the size of the test and is 1 minus the specificity of the test. It should also be noted that α (alpha) is sometimes referred to as the confidence of the test, or the level of significance (LOS) of the test. For a Type II error, it is shown as β (beta) and is 1 minus the power or 1 minus the sensitivity of the test. Statistical and econometric modelling[edit] The fitting of many models in statistics and econometrics usually seeks to minimise the difference between observed and predicted or theoretical values. This difference is known as an error, though when observed it would be better described as a residual. The error is taken to be a random variable and as such has a probability distribution. Thus distribution can be used to cal
be challenged and removed. (March 2013) (Learn how and when to remove this template message) In digital transmission, the number of bit errors is the number of received bits of a data stream over a communication channel that have been altered due probability of error for qpsk to noise, interference, distortion or bit synchronization errors. The bit error rate (BER) is the probability of error calculation in digital communication number of bit errors per unit time. The bit error ratio (also BER) is the number of bit errors divided by the probability of error binary symmetric channel total number of transferred bits during a studied time interval. BER is a unitless performance measure, often expressed as a percentage.[1] The bit error probability pe is the expectation value of the bit error ratio. The bit https://en.wikipedia.org/wiki/Probability_of_error error ratio can be considered as an approximate estimate of the bit error probability. This estimate is accurate for a long time interval and a high number of bit errors. Contents 1 Example 2 Packet error ratio 3 Factors affecting the BER 4 Analysis of the BER 5 Mathematical draft 6 Bit error rate test 6.1 Common types of BERT stress patterns 7 Bit error rate tester 8 See also 9 References 10 External links https://en.wikipedia.org/wiki/Bit_error_rate Example[edit] As an example, assume this transmitted bit sequence: 0 1 1 0 0 0 1 0 1 1 and the following received bit sequence: 0 0 1 0 1 0 1 0 0 1, The number of bit errors (the underlined bits) is, in this case, 3. The BER is 3 incorrect bits divided by 10 transferred bits, resulting in a BER of 0.3 or 30%. Packet error ratio[edit] The packet error ratio (PER) is the number of incorrectly received data packets divided by the total number of received packets. A packet is declared incorrect if at least one bit is erroneous. The expectation value of the PER is denoted packet error probability pp, which for a data packet length of N bits can be expressed as p p = 1 − ( 1 − p e ) N {\displaystyle p_{p}=1-(1-p_{e})^{N}} , assuming that the bit errors are independent of each other. For small bit error probabilities, this is approximately p p ≈ p e N . {\displaystyle p_{p}\approx p_{e}N.} Similar measurements can be carried out for the transmission of frames, blocks, or symbols. Factors affecting the BER[edit] In a communication system, the receiver side BER may be affected by transmission channel noise, interference, distortion, bit synchronization problems, attenuation, wireless multipath fading, etc. The BER may be improved by choosi
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