The document discusses simulation as an important tool for statistical computation. It describes how simulation allows researchers to (1) reproduce randomness on computers, (2) determine probabilistic properties of statistical procedures, and (3) approximate integrals and maximize functions. The key components of simulation include pseudo-random number generators that produce uniform random variables, which are then used to simulate other probabilistic processes and systems.
Zaborac Counseling Group came to us for a whole new image; new type treatment for their logo, new brochure, new business cards and new advertising. The Group is well-established and trusted, with Doreen Zaborac a recognized expert in her field.
Incorporating the colors, theme and ambiance of the physical location of the Group, we designed a warm, welcoming, easy to read brochure with a simple, classical logo in place. We strengthened the brand with business cards and advertising that support the colors, layout and feel of the mission brochure and logo.
ASPEC Sales Productivity App for the iPhoneSalesWays
The patented and proven ASPEC Sales Methodology lays the foundation for your sales processes. ASPEC apps put your skills to use in the right way at the right time, on your iPhone or in the Cloud. The SalesWays Hub is a community of sales professionals who contribute knowledge and new thinking for the modern sales professional.
It's all there in The ASPEC Experience.
Learn more at http://www.salesways.com
ASPEC Mobile is a powerful, free iPhone sales app for solo sales professionals, sales teams, and enterprise sales organizations.
ASPEC Cloud is a web-based sales tracking application for opportunity management. A complete sales productivity system, ASPEC Cloud elegantly prioritizes the list of opportunities, makes forecasting a breeze, and improves sales performance.
Zaborac Counseling Group came to us for a whole new image; new type treatment for their logo, new brochure, new business cards and new advertising. The Group is well-established and trusted, with Doreen Zaborac a recognized expert in her field.
Incorporating the colors, theme and ambiance of the physical location of the Group, we designed a warm, welcoming, easy to read brochure with a simple, classical logo in place. We strengthened the brand with business cards and advertising that support the colors, layout and feel of the mission brochure and logo.
ASPEC Sales Productivity App for the iPhoneSalesWays
The patented and proven ASPEC Sales Methodology lays the foundation for your sales processes. ASPEC apps put your skills to use in the right way at the right time, on your iPhone or in the Cloud. The SalesWays Hub is a community of sales professionals who contribute knowledge and new thinking for the modern sales professional.
It's all there in The ASPEC Experience.
Learn more at http://www.salesways.com
ASPEC Mobile is a powerful, free iPhone sales app for solo sales professionals, sales teams, and enterprise sales organizations.
ASPEC Cloud is a web-based sales tracking application for opportunity management. A complete sales productivity system, ASPEC Cloud elegantly prioritizes the list of opportunities, makes forecasting a breeze, and improves sales performance.
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...Ramesh Iyer
In today's fast-changing business world, Companies that adapt and embrace new ideas often need help to keep up with the competition. However, fostering a culture of innovation takes much work. It takes vision, leadership and willingness to take risks in the right proportion. Sachin Dev Duggal, co-founder of Builder.ai, has perfected the art of this balance, creating a company culture where creativity and growth are nurtured at each stage.
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Connector Corner: Automate dynamic content and events by pushing a buttonDianaGray10
Here is something new! In our next Connector Corner webinar, we will demonstrate how you can use a single workflow to:
Create a campaign using Mailchimp with merge tags/fields
Send an interactive Slack channel message (using buttons)
Have the message received by managers and peers along with a test email for review
But there’s more:
In a second workflow supporting the same use case, you’ll see:
Your campaign sent to target colleagues for approval
If the “Approve” button is clicked, a Jira/Zendesk ticket is created for the marketing design team
But—if the “Reject” button is pushed, colleagues will be alerted via Slack message
Join us to learn more about this new, human-in-the-loop capability, brought to you by Integration Service connectors.
And...
Speakers:
Akshay Agnihotri, Product Manager
Charlie Greenberg, Host
Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
Sr Director, Infrastructure Ecosystem, Arm.
The key trends across hardware, cloud and open-source; exploring how these areas are likely to mature and develop over the short and long-term, and then considering how organisations can position themselves to adapt and thrive.
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...Ramesh Iyer
In today's fast-changing business world, Companies that adapt and embrace new ideas often need help to keep up with the competition. However, fostering a culture of innovation takes much work. It takes vision, leadership and willingness to take risks in the right proportion. Sachin Dev Duggal, co-founder of Builder.ai, has perfected the art of this balance, creating a company culture where creativity and growth are nurtured at each stage.
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Connector Corner: Automate dynamic content and events by pushing a buttonDianaGray10
Here is something new! In our next Connector Corner webinar, we will demonstrate how you can use a single workflow to:
Create a campaign using Mailchimp with merge tags/fields
Send an interactive Slack channel message (using buttons)
Have the message received by managers and peers along with a test email for review
But there’s more:
In a second workflow supporting the same use case, you’ll see:
Your campaign sent to target colleagues for approval
If the “Approve” button is clicked, a Jira/Zendesk ticket is created for the marketing design team
But—if the “Reject” button is pushed, colleagues will be alerted via Slack message
Join us to learn more about this new, human-in-the-loop capability, brought to you by Integration Service connectors.
And...
Speakers:
Akshay Agnihotri, Product Manager
Charlie Greenberg, Host
Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
Sr Director, Infrastructure Ecosystem, Arm.
The key trends across hardware, cloud and open-source; exploring how these areas are likely to mature and develop over the short and long-term, and then considering how organisations can position themselves to adapt and thrive.
Dev Dives: Train smarter, not harder – active learning and UiPath LLMs for do...UiPathCommunity
💥 Speed, accuracy, and scaling – discover the superpowers of GenAI in action with UiPath Document Understanding and Communications Mining™:
See how to accelerate model training and optimize model performance with active learning
Learn about the latest enhancements to out-of-the-box document processing – with little to no training required
Get an exclusive demo of the new family of UiPath LLMs – GenAI models specialized for processing different types of documents and messages
This is a hands-on session specifically designed for automation developers and AI enthusiasts seeking to enhance their knowledge in leveraging the latest intelligent document processing capabilities offered by UiPath.
Speakers:
👨🏫 Andras Palfi, Senior Product Manager, UiPath
👩🏫 Lenka Dulovicova, Product Program Manager, UiPath
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...DanBrown980551
Do you want to learn how to model and simulate an electrical network from scratch in under an hour?
Then welcome to this PowSyBl workshop, hosted by Rte, the French Transmission System Operator (TSO)!
During the webinar, you will discover the PowSyBl ecosystem as well as handle and study an electrical network through an interactive Python notebook.
PowSyBl is an open source project hosted by LF Energy, which offers a comprehensive set of features for electrical grid modelling and simulation. Among other advanced features, PowSyBl provides:
- A fully editable and extendable library for grid component modelling;
- Visualization tools to display your network;
- Grid simulation tools, such as power flows, security analyses (with or without remedial actions) and sensitivity analyses;
The framework is mostly written in Java, with a Python binding so that Python developers can access PowSyBl functionalities as well.
What you will learn during the webinar:
- For beginners: discover PowSyBl's functionalities through a quick general presentation and the notebook, without needing any expert coding skills;
- For advanced developers: master the skills to efficiently apply PowSyBl functionalities to your real-world scenarios.
Search and Society: Reimagining Information Access for Radical FuturesBhaskar Mitra
The field of Information retrieval (IR) is currently undergoing a transformative shift, at least partly due to the emerging applications of generative AI to information access. In this talk, we will deliberate on the sociotechnical implications of generative AI for information access. We will argue that there is both a critical necessity and an exciting opportunity for the IR community to re-center our research agendas on societal needs while dismantling the artificial separation between the work on fairness, accountability, transparency, and ethics in IR and the rest of IR research. Instead of adopting a reactionary strategy of trying to mitigate potential social harms from emerging technologies, the community should aim to proactively set the research agenda for the kinds of systems we should build inspired by diverse explicitly stated sociotechnical imaginaries. The sociotechnical imaginaries that underpin the design and development of information access technologies needs to be explicitly articulated, and we need to develop theories of change in context of these diverse perspectives. Our guiding future imaginaries must be informed by other academic fields, such as democratic theory and critical theory, and should be co-developed with social science scholars, legal scholars, civil rights and social justice activists, and artists, among others.
JMeter webinar - integration with InfluxDB and GrafanaRTTS
Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
JMeter webinar - integration with InfluxDB and Grafana
Simulation - public lecture
1. Simulation: an ubiquitous tool for statistical computation
Simulation: an ubiquitous tool for statistical
computation
Christian P. Robert
Universit´ Paris-Dauphine, IUF, & CREST
e
http://www.ceremade.dauphine.fr/~xian
July 9, 2012
2. Simulation: an ubiquitous tool for statistical computation
Outline
Simulation, what’s that for?!
Producing randomness by deterministic means
Monte Carlo principles
Simulated annealing
3. Simulation: an ubiquitous tool for statistical computation
Simulation, what’s that for?!
Illustrations
Necessity to “(re)produce chance” on a computer
Evaluation of the behaviour of a complex system (network,
computer program, queue, particle system, atmosphere,
epidemics, economic actions, &tc)
[ c Office of Oceanic and Atmospheric Research]
4. Simulation: an ubiquitous tool for statistical computation
Simulation, what’s that for?!
Illustrations
Necessity to “(re)produce chance” on a computer
Production of changing landscapes, characters, behaviours in
computer games and flight simulators
[ c guides.ign.com]
5. Simulation: an ubiquitous tool for statistical computation
Simulation, what’s that for?!
Illustrations
Necessity to “(re)produce chance” on a computer
Determine probabilistic properties of a new statistical
procedure or under an unknown distribution [bootstrap]
(left) Estimation of the cdf F from a normal sample of 100 points;
(right) variation of this estimation over 200 normal samples
6. Simulation: an ubiquitous tool for statistical computation
Simulation, what’s that for?!
Illustrations
Necessity to “(re)produce chance” on a computer
Validation of a probabilistic model
Histogram of 103 variates from a distribution and fit by this distribution density
7. Simulation: an ubiquitous tool for statistical computation
Simulation, what’s that for?!
Illustrations
Necessity to “(re)produce chance” on a computer
Approximation of a integral
[ c my daughter’s math book]
8. Simulation: an ubiquitous tool for statistical computation
Simulation, what’s that for?!
Illustrations
Necessity to “(re)produce chance” on a computer
Maximisation of a weakly regular function/likelihood
[ c Dan Rice Sudoku blog]
9. Simulation: an ubiquitous tool for statistical computation
Simulation, what’s that for?!
Illustrations
Necessity to “(re)produce chance” on a computer
Pricing of a complex financial product (exotic options)
Simulation of a Garch(1,1) process and of its volatility (103 time units)
10. Simulation: an ubiquitous tool for statistical computation
Producing randomness by deterministic means
Pseudo-random generator
Pivotal element/building block of simulation: always requires
availability of uniform U (0, 1) random variables
[ c MMP World]
11. Simulation: an ubiquitous tool for statistical computation
Producing randomness by deterministic means
Pseudo-random generator
Pivotal element/building block of simulation: always requires
availability of uniform U (0, 1) random variables
0.1333139
0.3026299
0.4342966
0.2395357
0.3223723
0.8531162
0.3921457
0.7625259
0.1701947
0.2816627
.
.
.
12. Simulation: an ubiquitous tool for statistical computation
Producing randomness by deterministic means
Pseudo-random generator
Pivotal element/building block of simulation: always requires
availability of uniform U (0, 1) random variables
Definition (Pseudo-random generator)
A pseudo-random generator is a deterministic function f from ]0, 1[
to ]0, 1[ such that, for any starting value u0 and any n, the
sequence
{u0 , f(u0 ), f(f(u0 )), . . . , f n (u0 )}
behaves (statistically) like an iid U (0, 1) sequence
13. Simulation: an ubiquitous tool for statistical computation
Producing randomness by deterministic means
Pseudo-random generator
Pivotal element/building block of simulation: always requires
availability of uniform U (0, 1) random variables
q
0.8 q
q
0.6
xt+1
q
0.4
q
q
0.2
q
q
q
0.0
0.0 0.2 0.4 0.6 0.8
10 steps (ut , ut+1 ) of a uniform generator
14. Simulation: an ubiquitous tool for statistical computation
Producing randomness by deterministic means
Philosophical foray
¡Paradox!
While avoiding randomness, the deterministic sequence
(u0 , u1 = f(u0 ), . . . , un = f(un−1 ))
must resemble a random sequence!
Debate on whether or not true
randomness does exist (Laplace’s
demon versus Schroedinger’s
cat), in which case pseudo
random generators are not
random (von Neuman’s state of
sin)
15. Simulation: an ubiquitous tool for statistical computation
Producing randomness by deterministic means
Philosophical foray
¡Paradox!
While avoiding randomness, the deterministic sequence
(u0 , u1 = f(u0 ), . . . , un = f(un−1 ))
must resemble a random sequence!
Debate on whether or not true
randomness does exist (Laplace’s
demon versus Schroedinger’s
cat), in which case pseudo
random generators are not
random (von Neuman’s state of
sin)
16. Simulation: an ubiquitous tool for statistical computation
Producing randomness by deterministic means
Philosophical foray
¡Paradox!
While avoiding randomness, the deterministic sequence
(u0 , u1 = f(u0 ), . . . , un = f(un−1 ))
must resemble a random sequence!
Debate on whether or not true
randomness does exist (Laplace’s
demon versus Schroedinger’s
cat), in which case pseudo
random generators are not
random (von Neuman’s state of
sin)
17. Simulation: an ubiquitous tool for statistical computation
Producing randomness by deterministic means
Philosophical foray
¡Paradox!
While avoiding randomness, the deterministic sequence
(u0 , u1 = f(u0 ), . . . , un = f(un−1 ))
must resemble a random sequence!
Debate on whether or not true
randomness does exist (Laplace’s
demon versus Schroedinger’s
cat), in which case pseudo
random generators are not
random (von Neuman’s state of
sin)
18. Simulation: an ubiquitous tool for statistical computation
Producing randomness by deterministic means
True random generators
Intel circuit producing “truly random” numbers:
There is no reason physical generators should be
“more” random than congruential (deterministic)
pseudo-random generators, as those are valid
generators, i.e. their distribution is exactly known
(e.g., uniform) and, in the case of parallel
generations, completely independent
19. Simulation: an ubiquitous tool for statistical computation
Producing randomness by deterministic means
True random generators
Intel generator satisfies all benchmarks of
“randomness” maintained by NIST:
Skepticism about physical devices, when compared
with mathematical functions, because of (a)
non-reproducibility and (b) instability of the device,
which means that proven uniformity at time t does
not induce uniformity at time t + 1
20. Simulation: an ubiquitous tool for statistical computation
Producing randomness by deterministic means
A standard uniform generator
The congruencial generator on {1, 2, . . . , M}
f(x) = (ax + b) mod (M)
has a period equal to M for proper choices of (a, b) and becomes a
generator on ]0, 1[ when dividing by M + 1
21. Simulation: an ubiquitous tool for statistical computation
Producing randomness by deterministic means
A standard uniform generator
The congruencial generator on {1, 2, . . . , M}
f(x) = (ax + b) mod (M)
has a period equal to M for proper choices of (a, b) and becomes a
generator on ]0, 1[ when dividing by M + 1
Example
Take
f(x) = (69069069x + 12345) mod (232 )
and produce
... 518974515 2498053016 1113825472 1109377984 ...
i.e.
... 0.1208332 0.5816233 0.2593327 0.2582972 ...
22. Simulation: an ubiquitous tool for statistical computation
Producing randomness by deterministic means
A standard uniform generator
The congruencial generator on {1, 2, . . . , M}
f(x) = (ax + b) mod (M)
has a period equal to M for proper choices of (a, b) and becomes a
generator on ]0, 1[ when dividing by M + 1
23. Simulation: an ubiquitous tool for statistical computation
Producing randomness by deterministic means
A standard uniform generator
The congruencial generator on {1, 2, . . . , M}
f(x) = (ax + b) mod (M)
has a period equal to M for proper choices of (a, b) and becomes a
generator on ]0, 1[ when dividing by M + 1
24. Simulation: an ubiquitous tool for statistical computation
Producing randomness by deterministic means
Approximating π
My daughter’s pseudo-code:
N=1000
π=0
ˆ
for I=1,N do
X=RDN(1), Y=RDN(1)
if X2 + Y2 < 1 then
π = π+1
ˆ ˆ
end if
end for
return 4*ˆ /N
π